In the footage apparently taken from a passing vehicle, the driver can be seen veering off the road before crashing into some trees in the McKinney area north of Dallas.
The local Teamsters union says the truck did not have air conditioning, and the driver was kept on the job even after he told his bosses he wasn't feeling well.
In a statement, UPS says it cares deeply about the driver's safety. The company also says it is equipping all new vehicles with AC and modifying existing ones.
The driver was taken to the hospital and since been released, according to the union.