Purpose of heat engine is to transfer heat into the useful work, basically. Working object either gas or liquid takes heat from a thermal energy reservoir as a result of which their internal energy increases and this energy is somehow used to do work. Why would we need a cold body then?
Answer
The heat engine is assumed to be brought back to it's original thermodynamic state, after each cycle of operation. That is, in particular, the operation is reversible, with the net change in entropy of the engine being 0.
The net change in internal energy $U$ and entropy $S$ have to be $0$, after a cycle of operation. The net energy change is indeed zero, considering that the work done is equivalent to the net heat taken in. For the entropy change to be zero, it has to get rid of some of the heat it took in, in the form of heat itself.
In order to maximize the amount of work done, it may expel heat at a very low temperature, so it has to give out as little heat as possible; but give out some heat it must, to the cold body.
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