Q: Aircon problem. When a/c gas is empty, the engine temperature rise from 88 to 105 c. If a/c system works fine, temperature is ok

My car is having aircon gas leaking. When the gas is empty and blowing hot air, automatically the engine coolant temperature rising from normal 89 Celsius to 106 Celsius. When the aircon gas is empty, the radiator fan only rotates at lowest speed.

I refilled the aircon gas, it's cold and engine coolant temperature back to normal. The radiator fan back to normal and could rotates in maximum speed.

Thermostat, coolant level, all normal.

What the correlation between faulty aircon and rising engine coolant temperature?

I can hear loud hissing sound from dashboard. Do you think evaporator / cooling coil is faulty?

Thanks

My car has 124000 miles.
My car has an automatic transmission.