I'm investigating a material, that under high temperature-pressure conditions undergoes a phase transition. In order to correctly calculate the temperature, or even estimate a reasonable value, I need to know the specific heat of the material post phase transition. Unfortunately these values haven't been determined for the materials I'm interested in, and I'm not in a position to easily determine them experimentally.
My question then is, do reasonably straightforward techniques exist for the estimation of specific heat of fairly arbitrary materials? I suspect I could look at molecular dynamics or atomistic techniques, but these feel as involved as doing the work experimentally.
Edit with some extra information
The phase change is solid-solid, and compression to the high PT state occurs sufficently quickly that isothermal conditions, or temperature control are not credible. I can't say which material I'm interested in exactly due to commerical confidence, but sucrose is a not unreasonable analogue.