If your car is running hot but not overheating then the most common cause of the car running hot but not actually overheating is due to a faulty thermostat in your engine.
The vehicle's thermostat is responsible for regulating the amount of coolant flowing through the engine from the radiator and when it's stuck closed it can cause the engine temperature to increase and result in a cars engine overheating or just running hot without overheating.
To replace the thermostat you need to drain the coolant down and remove the radiator hose which is the top radiator hose and the thermostat housing.
You'll also need a new thermostat housing gasket to seal the thermostat housing again.
Another cause could be low engine coolant level in the engine or your cooling fans may not be operating properly when they need too.
Or even low oil level can also cause a car to run a bit hot and not overheat.
As long as your engine is not getting to the overheating stage then it's okay to drive the car but you should have it checked out to prevent engine damage if the temperature begins to rise to where it would overheat.
If your engine overheats or begins to overheat you should shut the engine off to prevent damage to the engine.