I have a converted 10 gallon igloo cooler for my mash tun and I have tried preheating vs higher strike water temperatures to maintain a consistent mash temperature several times.
With all the times I’ve tried this in my set up it seems that preheating the tun is the way to go. It may seem small if the temperature only varies in a few degrees but those few degrees have screwed up my efficiencies on several batches.
All I do to heat mine up is heat about a gallon of water to 200°F and toss it in the tun and let it sit for about 20 mins with the lid on. I don’t heat it to the boiling point as to reduce wear and tear on my cooler, the boiling temp is a bit too high for it and can potentially warp it.
This works well for me anyway since I’m waiting for the other 6 or so gallons of water to hit the right temperature I’m looking for.