[spand]

Not sure of the total outcome but the heat source might not be as efficient at pumping out heat for it to get warm quickly enough than it would at a constant rate. I cannot find a source now but I believe this is even the case for new refrigerators that they run in a much more continuous mode than the jagged cool/off mode.

[distances]

I suppose that's possible with some special cases, I wouldn't really know. This type of energy loss would be quite different from the claim parent mentioned about "stored heat" though.