Check your fan clutch
Two things you may want to do:
1. Flush your cooling system
2. Check your fan clutch.
3. If the fan runs, then it's ok and doesn't need replacement like the mechanic said. Those fan last a long time without problems.
4. The fan should run at low speed the minutes you turn the A/C on. When the temp goes high, the fan comes on at high speed.
To me it sounds like your fan clutch is a little week and not engaging properly when the temperature goes up.
1993 190E 2.6
Advanced Diesel Systems Test and Research Engineer