The 6000 shouldn't have any problems with heat as high as 90, I just drove from Florida back to Texas in a lot higher heat than that and had no problems.
I did have the same error message on the way there though, stupid me assumed that when you take a generator in for service that they actually put fluid Back into the thing before sending you on your way.
Kept running for 10-15 minutes and shutting down on high heat but I was only checking the overflow, had no idea the thing was totally without coolant in the radiator.
Don't make my same mistake and assume since the overflow tank has coolant the radiator does.
A gallon of coolant later the thing ran fine all the way back home.