Dashboard temperature overheating when A/C is on

I have a 1999 VT Berlina 2.
Yesterday the dashboard temperature sensor showed overheating, so I stopped the car and checked under the hood. The engine, coolant and radiator were fine. No signs of coolant leaking.

Went back in the car and started her up without the air conditioner on (it was on heat mode coz Brissy has been cold these few days). The temp gauge slowly went back to normal and I managed to drive the car back home.

At home I turned on the A/C again and the temp gauge quickly raised again. Turned off the A/C and it decreased back to normal (quickly).

I've been reading some posts on coolant leaking, water pump failing, coolant temp sensor and sender failing, but none actually relates to the A/C.

Before I take it to a mechanic, just thought I'd ask the forum if anyone has any ideas what the problem could be. Thanks for the help....