I'd check (replace actually) your thermostat first. At 124k miles - it wouldn't hurt to change it. It could not be opening fully - causing your woes. This shouldn't be that expensive.
If this has no effect - Thoroughly clean the cooling fins of your radiator.
If this has no effect - you may want to have your cooling system drained, flushed with a citrus "decalcifying" solution (MB makes such a product, I believe) and fill with proper coolant (the red MB stuff - NOT the green stuff).
Your coolant temp sensor sounds like it's working fine - as it is activating the fans when they are supposed to come on.
Let us know how you do.
1995 E420 72k