This is a nice simple solution. 4 modified power cords and 3 relays. Thanks! I am kicking my self for not thinking of it myself.

Thanks. I'm glad I could help!

 

How can that advice in post #20 be simpler when it requires connecting downstream of each sensor associated with the heating system or the cooling system. A single in-line sensor detecting the current draw, using a tried and proven approach, would be simpler.
Of course, this is based on the heating and cooling systems being separate, and each having it's own sensor as part of that system. If the temperature control portion is entirely separate from the heating and cooling equipment, and if that sensing system switches the power to each function quite externally, then is certainly applicable.

So once again we have an example of only a small portion of the context of the question being presented and the lack of context making the obvious solution much more challenging to discover.

I did finally look at the controller link in post #4 and I see that it already has two controlled outlets available. So one can power the heater/cooler device and the other can power the controlling relay for the mister, with no need to modify any power cord. Just plug and play. And it occurs to me that instead of three relays wired with contacts in parallel, three lights illuminating one photo switch could work, if a photo switch that switched ON when illuminated could be found.

If it had been clear from the start that every controller was a separate block, the answer to the concern would have been determined much sooner.