Mark, a few things off the top of my head
Firstly both the control and the test subject need similar properties such as heat capacity, conductivity and density. I am thinking in terms of thermal mass (heat up rates) which will affect the outcome of the experiment
Secondly, accurate thermal measurement may prove difficult, what method would you propose to use?
Thirdly, the type of heat transfer from environment to object may be a factor. For example, the surface of the crystal (roughness, porosity) might aid or hinder convective heat transfer. The opacity and reflective properties will have an effect on radiative transfer.
Probably better to go from freezer to pre-heated oven.
Just a thought ???