The OP seems to have ignored many of the points that I've made in this thread, so this will be my last intrusion into this thread.
The problem here in the very beginning is (i) the faulty starting point, i.e. the OP made arbitrary comparison between the process of heating and cooling, and (ii) the conclusion derived from that faulty starting point.
This can be a lesson to many people, especially non-scientists, in how we devise a valid experiment to test a hypothesis. This is especially true when we want to make a comparison between two different processes, in this case, heating and cooling. Is it a fair comparison to heat something on a burner, and then compare that to cooling it in a refrigerator? I've posted on why it is not.
IF the whole issue here is to see how "easy" or "difficult" it is to heat or cool something, then the process of cooling and heating must be as close to be identical as possible. Otherwise, other factors will come in that has nothing to do with the physics of heating and cooling that substance. In other words, we want the heating and cooling of the object to be INDEPENDENT of the process that we use, so that we can get to the actual physics and detect if there are differences in the two processes that are NOT due to how we heat and cool it.
So, similar to what I've suggested before, here's what we can do:
1. Get a 1 kg mass of water in a metal vessel.
2. Let it come to thermal equilibrium at room temperature, say 20 C.
3. Immerse it in a heat bath that is at 30 C.
4. Record the time it takes for the water to get to 30 C.
5. Repeat the experiment, but this time, immerse it in a cold bath that is at 10 C.
6. Record time it takes for the water to come to 10 C.
7. Compare the time. If they are the same, then the process of heating and cooling is identical. If they are not, then you have something.
I pick the same temperature difference to heat and cool to make sure that the rate of heat loss or heat absorption due to surrounding temperature will be similar, i.e. one must make sure that external factors do not significantly affect the result.
If there is a noticeable difference in the time taken for cooling and heating, then this thread is valid. If not, then this thread is moot, because we will be trying to discuss why the unicorn has pink horn.
With that, I'm done!
Zz.