First stop the engine and let it cool down for 10 - 20 minutes. Next, check the coolant level in the reservoir and check for signs of a leak. Check if the electric radiator fan is turning on when the temperature starts to get too high. If that is the problem, the engine will not overheat on the highway thanks to the natural air flow. Check for air bubbles in the reservoir when the engine is idling. That is a sign of a leaking cylinder head gasket. If the overheating is worse at highway speeds, check the radiator for signs the cooling fins are corroded and crumbling away.

You don't have the heater turned on, but it's on anyway. The heater works by taking hot coolant from the engine and cycling that through a heat exchanger in the blower housing. There's another exchanger (called an evaporator) that serves the AC - lot of stuff going on in that housing. But the heater control lever is attached to a valve that sends hot coolant into the heater core. Either the lever's cable is broken, or stretched, or that valve is leaking - and I'm guessing it's that last one most of all, since at higher revs (above 30mph) the water pump makes enough pressure to push past the valve's bad seal. Whatever it is, the engine makes way more heat than the AC can pull out.