Just to be pedantic, but not exactly. The typical design in a domestic heating unit, or refrigerator is mechanical. A fluid is pumped and cyclically compressed/expanded. While electric motors are usually used, they can be driven by any source of mechanical energy; driven directly by a combustion engine is not too unusual.
There are also heat pump cycles that can be driven directly with heat. Refrigerators based on that are relatively common here in Canada in areas without reliable grid electricity. Usually a propane or natural gas flame.
Thermoelectric coolers are actual electric heat pumps; directly moving heat across a semiconductor junction. Not very efficient and quite expensive practically. They're used in those USB drink coolers and to cool down lab equipment. Finding a high-efficiency thermoelectric material that works at normal temperatures and pressures is nearly as much of a Holy Grail as finding a high temperature superconductor.