Regarding hatmana we know there are items that are mosif hevel. However it can’t be that these items actually give off heat, because simply placing them next to cold items doesn’t lead to them warming up those cold items in any way. It is only when the davar hamosif hevel is surrounding a hot item that it is somehow ’emitting heat’.
However it seems physically impossible for this to mean that the davar hamosif hevel is actually emitting heat. What then is the quality of mosif hevel? Is it that a mosif hevel retains and maybe ‘reflects back’ enough heat from the cooked and still hot item, to facilitate further cooking?
Or is it that ‘hevel’ doesn’t mean heat necessarily, but some other process. I have noticed that if you put olives in oil and spices in a closed container, eventually the plastic lid will pop off. Similarly with herring in oil and spices, often when left out the lid begins to blow up. THere is some reaction taking place that is giving off gas. Maybe the items which are mosif hevel give off gas when they become heated and this somehow facilitates the items staying hot or cooking in the manner that halacha does not permit?
These are just assumptions. But my main question is, it is not possible for a substance that is being heated by another substance to heat teh original source back more unless some kind of chemical reaction is taking place that begins to ignite the second substance. However, the items that are mosif hevel are not ignited or burning so as to be emitting their own heat.
You are right, not all of the cases in the Mishna are because of the same reason and type of heat. For example, Rashi says that the leftover olives give off a physical heat, (and possibly the leftover sesame), however regarding sand, the Ran and Ritva say that sand will only return the heat that it got, but it doesn’t have its own heat (as you wrote). On the other hand, some of the examples would be from a chemical heat, such as “sid”.