I would say it like- thermal power alludes to the energy contained inside a framework that is responsible for its temperature. Warmth is the progression of thermal power. Hoped this helped.
Thermal energy refers to several distinct physical concepts, such as the internal energy of a system; heat or sensible heat, which are defined as types of energy transfer; or for the characteristic energy of a degree of freedom in a thermal system kT, where T is temperature and k is the Boltzmann constant.
