It's probably the alternator belt. When you rev the engine it heats the belt up enough to grab the pulley. Then you get enough power to spin the fan motor at it's proper speed. I test the belt tension with my thumb. When I press hard in the middle of the longest span, it should deflect the belt less than a half-inch (~2cm). Not much at all, in other words.
If the belt is loose, find the alternator support bracket. It has a gear pattern stamped into it. The alternator is bolted to it. Loosen the nut on the rear of the alternator (13mm) and the bolts at the base (also 13mm). Then get a 17mm wrench & turn the large nut. It will tighten the belt. Don't overtighten that, it's easy to srip the gears on the bracket. If they're already stripped, use a prybar or large screwdriver to pry the alternator out instead. Then tighten everything up & test the tension again. If you run out of space and the belt is still loose, replace it. They can stretch over their life, and cheap parts are usually not sized correctly.
My e30 only has one belt left...the water pump/alt belt. I've pulled the other two!