Yes, a lack of coolant can cause your vehicle to run hotter when running the A/C. Try running the heater and see if the car cools down. Running the heater (yes, it will be hotter inside the truck) allows the engine to cool down a little more than normal. You might want to look into replacing the engine's thermostat. That's a low cost fix that sometimes helps run the vehicle at a lower temperature, even with the A/C running.
Not having coolant will cause a vehicle to run hot anytime.
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