"Thermal inertia" is more formally known as specific heat capacity or volumetric heat capacity, which is a substance's resistance to change in temperature.
It's similar to (but different from) mechanical inertia, which is an object's resistance to change in velocity.
The latter includes the concept of momentum, that an object with nonzero velocity resists changing it's velocity. There is no such thing as thermal momentum, remove the temperature differential and a thermally uniform substance that's changing temperature at 10 degrees per second will stop getting colder instantly. For related reasons, there's no overshoot when you reach equilibrium, either.
It's similar to (but different from) mechanical inertia, which is an object's resistance to change in velocity.
The latter includes the concept of momentum, that an object with nonzero velocity resists changing it's velocity. There is no such thing as thermal momentum, remove the temperature differential and a thermally uniform substance that's changing temperature at 10 degrees per second will stop getting colder instantly. For related reasons, there's no overshoot when you reach equilibrium, either.