Is there a set temperature that will be deemed too hot in my unit?

Each city sets its own codes regarding the maximum level the interior of the unit can be before it is deemed a code violation. Sometimes, those codes are based upon the type of cooling unit installed (e.g., air conditioner vs. swamp cooler) as well as the temperature outside (usually less than 20 degrees than outside).

EXAMPLE 1: The landlord provides a swamp cooler in a Phoenix apartment and the temperature is 115 degrees outside. In the City of Phoenix, a swamp cooler must cool to 86 degrees, or at least 20 degrees less than outside. The landlord must then ensure that the unit is cooling to at least 95 degrees inside.

EXAMPLE 2: If there is an air conditioning unit installed in a Phoenix apartment, the landlord must ensure that the premises cool to 82 degrees, or at least 20 degrees less than outside. If it is 105 degrees outside, the unit must cool to at least 85 degrees.

Resources

City of Phoenix Municipal Code - City of Phoenix Code art. II § 39-5(B)(1)(b) 

Air Conditioning Legal Info Sheet