Air temp is calculated using radiative dynamics. Skin is the same as metal in this regard. This is why we burn. Not to mention, if I had my shower set to deliver a measly 110 degree water, it would be on average about 5-10 degrees colder than the median air temp 9 months of the year where I live. And that isn't a dry heat as many non desert dwellers seem to believe.
Insufficient time-of-contact between dies and coin take place for significant heat transfer between the two. The dies and the press are incredibly large heat sinks, and absorb much more of the heat associated with each strike than do most of the planchets, until, of course, the day has been long, and the tooling and press have heated up a lot. The heat-treatment of the blanks does not take place immediately before striking. Typically, the planchets are annealed long before they even approach the presses. While the coins will indeed be warmer when ejected from the press, the dings you see on coins are from concentrated stress, imparted by edges and especially by reeding, whether impacted immediately after striking or long afterward.
I often suspect that a lot of the best strikes come from unusually warm planchets. There is probably a fairly wide range of temperatures that planchets can be from below freezing to as much as about 100 degrees. Most will be near room temperature but the range could be significant. I've always wondered what conditions have to exist for a perfect Gem to be minted. Of course a few more of these are produced than just what leaves the mint. These coins can be virtually non-existent for some dates.
I once put a lot of sunscreen in a box and lit the stuff inside to see what would happen I burned all the hair off my leg and arm
An interesting question. Bear in mind that, while the very best strikes may well be the result of recently annealed planchets, those are the very same coins that would likely take on the most marks after strike, so I wouldn't necessarily correlate the warmest planchets fed into the press with the highest quality coins to reach collectors hands.
When you talk about getting burned by metal. I was a welder for about 25+ years. I spot welded, brazed welded, mig welded, stick welded, and cut steel with a torch, and plasma cut metals too. So, getting burned and shot with hot metals of all kinds does hurt and leave many scars. Great job. Have been around die stamping presses too in the auto industry.
The planchets have to be washed and burnished after annealing, and they spend time sitting in bins and hoppers waiting to be fed into the press so they would be at room temperature by the time they get to the coining chamber.
I am certainly no expert in this field; however, from a physics standpoint, an increase in pressure while maintaining the same volume will increase the temperature. A common example of this is ice skating. Increasing the pressure(under the blades of the skate) increase the temperature of the ice, causing it to melt in the spot you are standing/skating allowing you to glide along. Sound right?