Car overheats only in very hot weather with air conditioner on
 

1990 ls400, 198,000 miles works fine. Our weather gets over 105 degrees F. When I drive home from work, around 30 miles, the air conditioner is on and my temperature gauge rises almost to the over-heat level. I turn my air conditioning off and it returns to normal quickly. This ONLY happens in VERY hot weather. Since it doesn't happen otherwise, I'd think my fan works. What else could be wrong?