I have two objects, A and B. A and B are identical in every way except their temperature. Units are not relevant: assume degrees C, F, or anything linear with them.
Also not relevant are phase transitions. Assume that either nothing is freezing/melting/otherwise, or at least that the effects are negligible. The matter is mostly or entirely in the same phase throughout the event.
The temperature of A is 100 degrees.
The temperature of B is 200 degrees.
Applying a heat source raises the temperature of A by 10 degrees up to 110 degrees.
With no modifications, the heat source is applied to B. Again, all other things being equal: should B be expected to heat up by 10 degrees also, or by some other amount?
For an example, consider a room that you want to warm with a fire. 1) The temperature of the room is 10 degrees and the addition of the fire warms it by 20 degrees up to 30 degrees. OR 2) The temperature of the room is actually -50 degrees, but will that same fire warm the room by 20 degrees up to -30?
I ask this because I thought the temperature change would be different in the two different situations. Taking the above example, I would have thought the -50 degree room would be warmed by more than 20 degrees (25? 30? I don't know, just more than 20.) But someone is telling me that the -50 degree room would be warmed by the same 20 degrees, not more.
My thought process is along these lines: Two objects will attempt to equalize their heat when brought together, so 10 degree water added to 30 degree water will result in approximately 20 degree water, but add that same water to 50 degree water and it will result in 30 degree water instead (+/- 20 instead of 10). I realize this is not the same as a heat source, but I thought something similar would apply.