BMW 3 Series overheating with cold air from hot heater

its do about 50k, recently the car blow out cold air with the heater on full hot , then the temp gauge went to the end of the red. naturally the car didnt start after i turned it off to cool down. took it to my mechanic for a service and told him of the issue.. he looked at the heat gasket , radiator( pritty new) , thermostat , and the hoses for any blockages. he replaced the thermostat which sorted the problem for 2 weeks when it happened again. its not losing any fluids and water level is fine.

if i start the car parked it will take about 5 mins to get up to the standard correct temp but after 20/30mins will suddenly start moving to the red where it will hit the end.

if i drive it at 30 in 5th i can keep the gauge just in the red ...just
if i drive it normally it will hit the end of the red in under 3 minutes.
could this be pump issues?

i know your ment to put hot air on full if your car overheats to get rid of some of the heat build up as i had a very temperamental pug 306... but mine just blows cold air?

also recently i smelt rotten eggs / gunpowder coming from the exhaust although i think this is a different problem ?

my mechanic is gona ask his mate that works for bmw if theres anything worth trying as he is confused. i decided to ask on here
any help would be ....helpful

thanks