For a little more of my personal perspective, as a new MP5, it's quite annoying to reduce heat. I actually recently used the wish Granos mentioned, a decision which I greatly regret. The only way I am really aware of to reduce heat is attacking popes, or leaving my trees in defense, each of which only give a few thousand heat reduction at a time. Whereas winning a normal fight against someone can give anywhere from 50k to 500k heat.
I've seen a few fights in the past where I lost 100k-200k heat, but I have no idea what triggered that. All of which has brought me to sort of give up on trying to advance my creatures or stats, at least for the time being until I find out how to reproduce those large heat losses. I honestly think the current heat system is quite demotivating for less experienced players who don't have the knowledge or the means to properly reduce it, and barring a total overhaul to the system, I support any addition that will make the mechanic less annoying.
That's just my 2 cents though.