On the contrary Dave, I just made a thread about this and there seems to be no harm in removing the heat shield. Since it is from under the car, I am assuming this is the heat shield around the catalytic converter. If that is indeed the case, then the heat shield is there to keep the cat hot so that the reactions taking place inside it take place more efficiently. Removing it at worst would harm your emissions.

Tack welding it would only be a temporary fix, when you consider that the heat shield is rattling because it is corroding. It can (and eventually will) just corrode more in spite of the welds and just start rattling again.

I would suggest taking it off and just be careful if you need to park in tall grass that it doesn't light the grass on fire.