Inertia is the resistance to change. It is particularly useful when thinking about forces and motion. It is a measure of how much a body (stationary or moving) does not want to accelerate. We can write Newtons second law as:
|Acceleration = ||force|
The force is what is trying to make the body accelerate (so it is on the top of the fraction). The mass is resisting the acceleration pushing a bigger mass will give it a smaller acceleration. In this case, the mass is a measure of the bodys inertia.
Thermal inertia, is how much something resists having its temperature raised:
|Temperature rise = ||heating|
The heating is trying to raise the temperature (on the top) and the heat capacity is resisting the change. The bigger the heat capacity, the more difficult it is to raise the temperature.