OK, here goes your thermal room in more acceptable format.
As for your question - I doubt there exists method of changing the temperature to store the heat that will meet your criteria - small, fast and efficient. Commonly used device is unit as used in freezers and heat pumps. However, to be efficient it must be bulky and it needs additional energy to operate.
Note that the fact such a device doesn't exist doesn't mean it was not invented yet, it is rather effect of very fundamental aspects of thermodynamics. Units used in freezers and heat pumps are developed for at least 80 years (perhaps even longer, no exact idea) and they are as efficient as it is possible. They can be made to work faster but they will neeed more energy operate and the energy is what you are trying to conserve.