The air conditioner will stop blowing cold air when requested.
Engine overheating with the AC on, especially in traffic, is a common side effect when the condenser cooling fan motor fails.
Common misdiagnoses
The air conditioning condenser cooling fan motor relay or fan control module is often mistakenly replaced when the fan motor does not function.
Since the air conditioner blows warm, erroneous addition of refrigerant to the system is common, but will only further complicate air conditioner issues.
Best practices
The condenser cooling fan motor is often sold as, and replaced as an assembly that includes the fan blades and housing.
Anytime a vehicle is overheated a shop should test for further engine damage.