> Isn't it harder to heat 32 degree air 1 degree than heat 70 degree air?

From a pure heat capacity viewpoint, heating cooler air is very slightly easier (on the order of a few thousandths at most for realistic temperatures) [0]. Don't think it'll be noticeable for the average heating system, though.

> we calculated everything, inefficiency, convection, conduction.

I'd be curious to how those calculations affect things. If the heating element is the same temperature, I'd think heating cooler air would be faster because heat conduction is faster across a larger temperature differential and you'd get "faster" convective mixing for air with bigger temperature differences. Have to admit I'm not sure what inefficiencies might come into play, and I haven't taken classes at that level so I wouldn't be surprised if I missed something.

[0]: https://www.engineeringtoolbox.com/air-specific-heat-capacit...

I could not find the problem I was referencing. I'm either wrong, or the problem wasn't in the book and was in the professors notes. I'm leaning on the later, but unless I reply with something else, assume I'm wrong.

Sorry to hear that you couldn't find the problem. Was hoping that I'd get to learn something new