The tune will cause a little more heat since the spark is retarded, but I never noticed any change on mine using that map. Even when ambient is >100F.
Interesting you had to add coolant. I suppose maybe it has a leak and the previous owner was topping off with the wrong kind?
I think an oem drive and then coolant flush is a great idea. If there is any gelled coolant, I wonder if it'll just come out, or be difficult?
Have fun on vacation!