In reply to Duncan Beard: It has been stated but not clearly,
A softshell is not as breathable as a good fleece.
If you need to manage the perspiration as effectively as possible then good quality light synthetic base layer will work best for moving moisture,
a thin fleece for boosting insulation if required, this can be called microfleece or 100 weight, again better quality ones move moisture better
and as others have suggested a pertex windtop or similar, this can be used just over base layer or over more insulation if required, again more breathable than alot of other types of softshell and more versatile as it has no lining to add to the heat,
If you get too hot you are wearing too many clothes, if he gets too hot in fleece wear a thinner fleece or dont wear it, try using windshell if chilly instead of fleece to stop overheating
HTH