given perfect heat pumps/engines in that circumstance, you would get exactly as much energy out as you put in. Theoretically perfect heat engines are called 're

given perfect heat pumps/engines in that circumstance, you would get exactly as much energy out as you put in. Theoretically perfect heat engines are called 'reversable' for that reason: they give you the best possible exchange between heat and work. Said another way: heat pumps can give you 4-5x the heat out as work you put in precisely for the same reason you can't get much work out of that heat: the temperature increase is small. If you were to heat something up to a temperature where you could more efficiently extract work from it, it would require more energy to do so.