when you turn A\C on, the engine bay gets hotter (heat is exchanged from the cabin to the engine bay) When you turn the cabin heater on, the engine coolant is being used to heat the air for the cabin blowers, helping your car to cool off.
BMW's weren’t meant to idle, A-la-007ben, you car likes air moving over it
and yes, do check for bugs and stuff on the radiator. Be gentle cleaning it off, they can spring leaks that you can't "fix".
Check thermostat, fluid level, and if your main engine crank fan clutch is worn out (it's easy to stop the fan [NOT WITH FINGERS! use a rolled up newspaper or something near the clutch] if the clutch is worn out)
there is also a common problem with E36's where the radiator top hose neck will crack. Mine cracked and BROKE off, ruining the radiator and expunging all the fluid out of my cooling system onto the road. That sucked.