I use this to get first estimate of what temp the strike water should be.
https://www.brewersfriend.com/mash/ I also know that for my equipment (pump + hoses from kettle to mashtun) I lose about 3F. My cooler only loses about 2F during a 60 minute mash, provided I only stir every ~10 minutes.
I don't preheat mashtun. I usually run all but 1-1.5 gallons of the strike water from the kettle into the mashtun, stir vigorously, give it a few minutes come to temp, and then take a measurement. If it's high, I swap that last gallon of strike water for a jug I keep in the fridge; similarly, if it's low, I superheat that last gallon and add it boiling.
Just don't do like my brew on Monday and use a broken thermometer... It said my strike water temp was 162F, so I ran it into the tun. When checking with an infrared gun, it said the temp was 132F..... Well ****, my $6 thermometer is broken. Ended up adding 3 whole extra gallons of boiling strike water to get to 151F. Made the efficiency suck too.
Side note: Any recommendations for a mashtun thermometer? Preferably something on a cord so that I can keep it outside the tun, and that's calibrate-able?