I agree with basket case. The blue foam is simply not a structural foam. It is designed specifically for cost effective insulating properties and it is substantially weaker in shear than the foams that are designed to be used in laminate cores. In a properly designed laminate, the core should largely resist shear loading. Use end grain balsa or the foams designed for composite core applications if you want to achieve reliable results. You will also find that you will get a much better bond to the foam (and a significantly better structure) with pressure applied to the laminate during cure (autoclave or vacuum).

I've had no heat issues with the West System epoxies...although almost all epoxies will get soft if you heat them to high temperatures. Also note that epoxies are affected by UV so if you are leaving them bare and exposed to the sun without a UV barrier, they will yellow and can get brittle.

If you really insist on cutting corners, you'll have better results using green rigid PVC foam from a floral shop than the blue stuff from a home improvement center.