Get out a torch (flashlight) and have a careful look at the condition of the belt. If it's shiny/glazed on the back side, or has cracks on the grooved side, it should be replaced. Also try to dig a fingernail into the back side of the belt - this should just be possible and the material should be slightly rough and 'grippy'. I know this is the back side and not the front side that does the driving, but if the back side is hard and glazed, the front side will almost certainly be similar.
It's possible that a small amount of water got on the belt and made it slip.
I prefer to replace the belt rather than to try and increase the tension of an old belt, because if you over-tension, you can wear out bearings.
By the way, my 2001 Sporting has two belts. One drives the alternator, and another drives the air conditioning compressor from the alternator pulley. The information in the Haynes manual for the Punto appears to be wrong, because it states that air-conditioned models have just the one belt and an automatic tensioner.
You could try removing the belt temporarily to see if the noise goes away. If not, then it could be something to do with the timing belt tensioner, and if that's the case, then it's important to investigate ASAP.
-Alex
