This may seem like a stupid question, but what role does moisture level play in the soils temp? My gut tells me water = colder soil, but perhaps the extra volume in the container keeps the roots warmer than a dryer soil?

I think the moisture level in soil itself does not play a direct role in soil temperature as water neither doesn't cool nor warm the soil. Soil is cooled by evaporation of water from it's surface (and also through container walls if you use f.e clay containers with porous walls). The evaporation rate in turn depends on the room temperature and air humidity - the warmer room and drier air, the higher the evaporation rate and cooling effect. A wet soil seems colder because it's thermal conductivity is better. And it may be colder indeed if not covered by drier mulch - due to higher evaporation rate.
Harri.

The heat capacity of water does also play a role. It takes 1 BTU (British Thermal Unit) to raise the temperature of 1 pound of water 1 degree F.

Barbara