Several people have given very good pieces of advice.
85-90 is probably an okay ambient temperature as long as their is air circulation like fans, and it's not just still, hot air cooking your rats.
And again, as several people mentioned, production rates can decrease as temperatures increase. You can look up scientific studies about rat and mouse fertility and litter rates in different temperatures. Labs all have their own specific number they like to keep their rodents at, but it's usually between 60 and 70 degrees.
Bringing in a single air conditioner would probably solve all of your problems. You can probably find one that would be effective for about $50, and then there would be no concerns about your rats.
The rats will also drink more, and therefore pee more, in hot conditions. This means you will need to clean more often because of ammonia build up. Not to mention the higher the temperature the more the ammonia will get into the air, which can cause respiratory distress without ventilation.
Several pet keepers that I know personally have had mice and rats die from heat exposure inside of their own homes, so it's not as if this is a myth.
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