Hi Bob,
If you had an issue with the alternator making the belt slip if a bearing was starting to fail the the noise would be there all the time, if you only get the noise just after startup then the belt may not be tight enough.
When you first start the car it takes a large amount of energy from the battery, as soon as the engine is started the alternator will try to replace the lost energy as quickly as possible putting a big load on the belt. At 80 amps the surface charge of the battery rapidly rises and the alternator output drops off taking the load off the belt.
I suspect the belt needs to be checked for the correct tension as the belt on the TF is only small in diameter (non AC version) A small amount of adjustment makes a big difference.
First step is check the tension as below and adjust if required.
Brian.