Estimation of specific heat of a solid 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.
 A: If your material is a pure substance and your final phase is a solid or gas, you could estimate the specific heat using the equipartition theorem as
$$
c_v = \frac{f}{2} \frac{R_\text{u}}{M} 
$$
where 


*

*$f$ is the number of internal degrees of freedom per particle, which is $6$ for a solid, $3$ for a monoatomic gas, and $5$ (at room temperature) or $7$ (at very high temperature) for a diatomic gas, but can also be evaluated for larger molecules,

*$R_\text{u}$ is the universal gas constant, and

*$M$ is the molar mass of the substance.

A: On the basis of the available information on the system, I would consider unsafe to use results from models in conditions where it is highly probable that strong anharmonicity and/or potentially unknown structural changes take place.
For a system not too different from sucrose, ab-initio simulations would be the method of choice to get reliable values for specific heat (which would not be a too difficult quantity to evaluate). 
I agree that performing an ab-initio simulation requires some specific expertise, but here we are moving out of the scientific ground. Maybe it could not be too difficult to find a person with the right expertise interested in working on the problem. 
