I am having a conceptual difficulty with heat engine efficiency. I do not understand why having a larger difference in temperature between the hot and cold reservoirs have an effect on the thermal efficiency. In this question I am specifically referring to Carnot heat engines. To clarify, I do not understand the reason the exact same (carnot) heat engine is more efficient when placed between different reservoirs. What is the mathematical or physical reason behind this?
I found this question: Why is it that a Carnot heat engine will reject no heat to a zero temperature sink? which is very similar to what I am asking, but the answers there don't make sense to me and it seems that was the case for the OP too.
I hope the question is clear and cheers in advance!