Which engine is in your Bug?

Is the coolant level correct? A mixture that is too rich in Antifreeze can turn the red warning light on... there is a level sensor in the bottle / reservoir
that "senses" fluid level, but can not do so if the mixture is too rich (should be 50/50 mix of antifreeze & water).

Check for correct coolant flow BACK into the bottle... at idle, you should see fluid flowing back in to the bottle:

http://www.youtube.com/watch?v=SJN3biTfdGE&feature=plcp

Sample of incorrect flow:

http://www.youtube.com/watch?v=thcwatH_BpI&feature=plcp

An "electrical glitch" or the wrong fluid mixture / level will cause and immediate flashing of the red light when cold... a mechanical issue such as a broken
water pump, will not cause the red light to flash until the engine has run for some time.

Sample of bad water pumps:

http://www.youtube.com/watch?v=WJlS7MvfRXo&feature=plcp

Thomas