The foam we have experience with is made by Dow ... and T2 will NOT melt it ...
http://building.dow.com/na/en/products/ ... idfoam.htm
These big box stores are convenient , but they really don't know what's going on with "experimental" things like this ... and you can get better materials and prices at something like an Insulating company that handles insulation for large projects like industrial coolers , etc...
The second problem is , the glue T2 cannot be used for construction , because it will not dry between two pieces of non-porus foam plastic (dries by evaporation ) so you'll need something like epoxy (or Gorilla glue) glue for joining the foam sheets .. which dries quickly and holds Very well ... For stitching pieces together , you can use a hot glue gun to "spot weld" ... but epoxy is the best for general construction ...
Now I know everybody's excited about using their old sheets for covering , and this would probably be fine for light duty (and Thrifty) there are a number of better alternatives... light weight canvas, or even light fiberglass cloth (2 oz.) attached with T2 will provide much more strength than a sheet ... just for those worried about towing at speed , we've built planes out of foam (for 10 years now ) that fly at speeds much faster than we could legally tow anything (or would want to @ 100mph +) ... These are constructed with Dow Blue foam , covered with everything from brown Kraft paper, thin cardboard (non corrugated type ), silk, and light 3/4oz. fiberglass ( some with no covering at all) ... None have had a structural failure at speed ... and as far as planes go the foam holds up well in a crash , with only localized damage , easily repaired , because the foam is a homogenous material and the bad pieces can be cut away and new pieces inserted , without regard to grain (such as wood )..
Best thing with any foam construction is to obtain some scraps for test samples ... and do some experimenting with different glues , and coverings to see which ones You like the best , and give you some familiarity with the material ... cutting , sanding , etc.
I have some 1/2" Dow blu-foam ... I guess I could make a scale model of a TD just to prove the concept ... Might be a fun evenings project . and should answer most questions ...
Anybody wanting to see some of my foam planes can find them at
http://www.foamfly.com/gallery2/v/Photos/Glen/ and for further foam plane info ...
http://www.rcgroups.com/foamies-scratchbuilt-428/ Many ideas of foam construction ... all applicable to foamie TD building ...