Old carb engine on VW Polo 1982 over heating.

Could just be a short circuit on the gauge wiring. Does it go straight to the red immediately? even when started from cold? If so, it's unlikely to be giving you an accurate reading.
The gauge on my 80s golf is pretty temperamental, but normally doesn't work rather than giving crazy high temp. Dunno if you have an electric fan or not, but if so, that's a separate temp sensor, so if the fan is coming on too, that's a sign the engine is actually hot and the temp gauge is telling you the truth.

Obviously check your water levels, could just be low/you could have a leak and for mayo in the oil cap which is a sign of head gasket failure.

The mechanic will probably just chuck a new thermostat in it, back flush the rad and the block, And make sure the heater is bled too.

Does the heater work? There is a bleed screw on the heater pipe under the scuttle cover, little white tap, You need to bleed the air out of it (get rid of the bubbles)

Mk2 polos do have a relitively small rad tho, And a small grille, They tend to run cool , But the temp soon shoots up as soon as you get to traffic, But the fan should cut in before that. The fan is pretty loud so you should be able to tell if its running.

Also being an 82 it should still likely have the radcap on the radiator rather than a seperate header tank, So might be worth bleeding it from there too.. Lots of air traps in these.. (ive had a few mk1's mk2's and a couple of mk3's ................................................. 15 )

Sounds like it's just a faulty reading. The gauges often work on resistance measurement. The sensor in the engine changes resistance depending on how hot it gets. The gauge measurers that resistance. If the wire to the sensor gets corroded or frayed the resistance will increase and the temp gauge on the dash will read much higher. So you've got a broken wire running between the sensor and the gauge, that's my guess.