When we talk about energy flowing between systems, we think of heat and work. Heat is energy that flows due to the temperature being different, and cannot be turned off. All you can do is increase the thermal isolation to increase the relaxation time. Work is energy that flows into a system that isn't due to a temperature difference. You can turn work on or off typically.
Playlist: • An Introduction to Thermal Physics by...
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The textbook I am using is: Schroeder, Daniel V. "An Introduction to Thermal Physics" 1st ed., Addison Wesley Longman, 2005.