My 2001 Toyota HiLux has been overheating when I use the air-conditioner

Air-conditioning can really add another layer of stress to an engine. Since the air-con compressor is driven off the engine (via a belt) it's just another thing for the engine to deal with. And since the engine has to make more power to run the air-con and travel at the same speed, it uses more fuel. And more fuel burned equals more heat, it's pretty basic physics to that point.

Any vehicle with a cooling system that is already a bit marginal can easily be made to overheat by switching on the air-conditioning. So the first thing to do is make sure there are no leaks in the cooling system, the radiator is not clogged internally or covered externally in dead bugs, the radiator hoses are not collapsing when you rev the engine, the water pump is working efficiently and the radiator cap is holding pressure (the boiling point of the coolant rises as you pressurise the system. Again, basic physics: Water boils at 100 degrees-C at sea level, but at the summit of Mount Everest, if you set up your camping stove, you'd boil water at just 68 degrees-C due to the lower atmospheric pressure).

The other thing to check is the condition of the cooling fans. The engine will have its own fan, but cars with air-conditioning usually have a second cooling fan that starts up when the air-con is switched on. You can tell if this second fan starts up by listening for it when you hit the A/C switch. If it isn't coming on (or the engine's fan is broken, slipping or doesn't have the correct shroud fitted) than this can easily lead to overheating.