How cool the engine runs has nothing really to do with the temperature of the incoming charge. It's ability to shed heat and the AFR are going to be the major contributors. Hot air is less dense, therefore the ecu will trim out fuel to keep the AFR where it should be. Sure the engine will run hotter in hot weather because of the differential between the cooling media, (Air and oil.) and the great lump of metal thet is trying to be cooled. Throw in the factors of fin area, cooler size, speed of travel and engine speed and there are a lot of variables but while in certain circumstances the motor will throw out a lot of waste heat it is engineered to take it without issue. It may be uncomfortable for the pilot but it won't hurt the engine.
I know Arizona is hot in summer, believe me Oz is scarcely frigid!
I've had to idle through slow traffic in 40+ degree heat regularly in Canberra. Been doing it for twelve years on my old lump. Never an issue.
Swapping to a well built open loop map will help a bit. I suggest you read up on Beetle's offerings and ask others here as to the efficacy of his products.