All manually adjusted belts should be checked for tension when the engine is hot, this is the reason manufacturuers have now turned to self adjusting belt tensioners, so the tension is linear and always correct nomatter what temp its at.

the belt may not actually be that slack when its cold, but when they run they often appear slack because of the slap effect on the longest side of the belt.

i see alot of belts fitted by other people here, and some even whine when they are hot, as they were tensioned up when cold.