Why must the operating temperature of a heat engine be higher than that of the cold sink?

It is important to note, that the 2nd Law of thermodynamics plays no fundamental role in answering this question; we need a heat sink because the entropy is a state function, and at the end of the reversible process (which is visualized through the Carnot cycle diagram relevant for this problem), the entropy value of the system must return to the value it had originally.