The story...

D.P.Grimmer wonders if thermite could have been used to melt box columns in the WTC, and after some calculations tells us...

...such a melting of a section of all the inner core box pillars is possible, using relatively simple technology. Such compounds could have been applied to the interior or the exterior of even the largest of these columns in a surreptitious manner, to accomplish the task of melting and collapse. The amount necessary for complete melting of a segment of even the largest box column was calculated, and found possible. Of course complete melting was not necessary to cause total failure: a lesser amount of a thermite-like compound could have been used to raise the temperature of the steel to a point where the columns would fail before melting, although some melting must have occurred to account for the steel pools.
http://www.physics911.ca/Grimmer:_Possible_Use_Of_Thermite_in_WTC

Our take...

Grimmer's article is commonly used to show that thermite could conceivably have been used to bring down the WTC. He comments on several reasons to suggest this hypothesis, including collapse time:

The observed near free-fall times of the WTC towers (and WTC7) were a dramatic signature of a controlled demolition. (The articles at http://members.fortunecity.com/911 are a valuable resource for presenting and then challenging the "official" explanation for WTC collapses). Measured times are all around 10 seconds, which is close to calculated free-fall time, indicating the tower floors fell without much impediment.
http://www.physics911.ca/Grimmer:_Possible_Use_Of_Thermite_in_WTC

Grimmer calculates what the collapse time should be if we allowed for the energy that will be lost in the creation of the dust clouds:

Now the observed time t = 10 seconds (a free fall time, the fastest possible time under g = 9.8 m/sec/sec = 32 ft/sec/sec = 32 ft/s exp2). For the cloud debris creation to absorb 30% of the gravitational energy, the observed time of fall would be 10s x 1.195, or almost 12 seconds. This long a collapse time was observed by no one. Clearly, there are serious flaws in the official explanation/conspiracy theory.
http://www.physics911.ca/Grimmer:_Possible_Use_Of_Thermite_in_WTC

Unfortunately for Grimmer's theory, "almost 12 seconds" is actually a short collapse time estimate, not a long one. There are seismic, video and audio clues that suggest the towers actually took something closer to 15 seconds to fall, perhaps even longer.

This undermines the very basis of Grimmer's paper, however we should still consider it. This is the only serious attempt to estimate the amount of thermite that might be required to bring down the WTC, and that means it still has some value.

And what is that amount? It varies depending on the column size, however we're told..

Thus to melt a 12 ft high Fe column, we need

for an "average" column, (3.03 x 10+6 kJ)/(3.974 x 10+3 kJ/kg) = 0.7625 x 10+3 kg = 762.5 kg of thermite...

for a "largest" column, (6.06 x10+6 kJ)/(3.974 x 10+3 kJ/kg) = 1524.9 kg thermite.
http://www.physics911.ca/Grimmer:_Possible_Use_Of_Thermite_in_WTC

762.5 kg/ 1,681 pounds? And only for one of the lesser columns? And how many columns would we have to melt? Four largest, 6 average size columns, for instance, gives us almost 9,150 kg/ around 20,000 pounds of thermite.

Still, Grimmer comes to the rescue by proposing how the thermite could have been placed. It might have been placed inside a box column, for instance. Getting it there may be problematic, so he also has another idea.

if a coating slightly less than 2" thick of a thermite coating were applied to the outer surface of any box column, that is sufficient chemical compound to melt that column section. A protective, insulating and cosmetic/disguising layer (e.g. fiberglass/foam) 1" or less would also be helpful.
http://www.physics911.ca/Grimmer:_Possible_Use_Of_Thermite_in_WTC

Plausible? Maybe not, because there are some important issues that Grimmer fails to address. (If you're up to the physics then please, read http://www.physics911.ca/Grimmer:_Possible_Use_Of_Thermite_in_WTC in full before continuing).

#1, Grimmer sets a single value for the specific heat (the amount of heat required to raise the temperature by one degree) of a box column. However...

The values of C [specific heat] do depend on temperature with those of common metals such as aluminum and brass increasing a few percent as the temperature increases from 20°C to 100°C, for example, while that for iron or steel increases about 10% over the same range.
http://www.physics.fsu.edu/users/ng/courses/phy2048c/lab/calorimetry/calorimetry.pdf

The specific heat increases with temperature, then. This means Grimmer requires more energy (and therefore more thermite) than he's suggesting.

#2, Grimmer appears to assume that the energy released by the thermite reaction will be used to heat the column. However, this seems unlikely, especially if it's coated around the outside of these colums. Even if the thermite is in turn covered with an "insulating layer" that's going to absorb some of the heat, then probably be destroyed by it. After that, what's going to stop heat radiating out into the surroundings? No account of that in Grimmers calculation, though, so again more thermite is required.

#3, there's no discussion here of what happens to the heat that does reach the steel column. Specifically, heat will be conducted away to other parts of the structure. Steel isn't a great conductor of heat, but this will happen to some degree, and as Grimmer doesn't account for it at all, then again it means more thermite must be added to the mix.

#4, for thermite to be used as a coating on the columns (and to stay there when burning) requires that it be made "sticky", presumably. How will this happen? If some other substance is added to the mix, then it may reduce the efficiency of the thermite reaction, again meaning you'd need more. Also, of course, it would again increase the volume of material required.

#5, there's no discussion of how long it will take for the thermite to burn, and whether that will be long enough to melt the steel. 

You can't necessarily address these issues in full by adding more thermite, either. Grimmer has this to say about the volume available for keeping thermite inside the largest sized box columns, for instance:

This would occupy a volume of 1524.9 kg/(3.974 x 10+3 kg/m3) = 0.439 m3. Note that this volume of thermFite also is less than the earlier calculated Vint = 0.529 m3
http://www.physics911.ca/Grimmer:_Possible_Use_Of_Thermite_in_WTC

Here he's pointing out that his estimated volume required is already close to the maximum amount of internal space available to store it. If it would actually take 21% more thermite than Grimmer's estimate then it would no longer fit inside the largest box columns. (The average sized ones have much more leeway and can hold "2.76 times more than needed to do the job", however if we took out only those then presumably we'd need to melt more columns overall).

The thermite coating idea doesn't necessarily save the day, either. You could add the same volume again, but as we've pointed out, that energy isn't all going to be directed into the column. The larger the coating of thermite, the bigger its surface area will be, and the more it will radiate heat away.

These objections cannot disprove the idea that thermite was used to bring down the towers, and that’s not why we raise them. They do show that Grimmer’s calculations omit many important factors, though, as well as failing to show that the setup methods he proposes are possible at all. Further analysis is required before any real conclusions can be made.