Alternators when charging do get pretty warm, maybe even to hot to touch, depending on the load - but ... they should not be so hot that they give off any smell or are obviously overheating!
An alternator getting extremely warm/hot are signs of other issues and should be checked.
A 12SI alternator will produce a 30~40A 12.5+VDC charge at @1000 RPM AT THE ALT.* - which is @600~700 Engine RPM
1st you should check voltage at both the output terminal of the alt. and at the battery - should be in the mid-12's at idle at both positions.
If it is low at bat. and correct at alt. then there is a bad connector or conductor between the two.
If it is low at both the the alt. is undercharging at idle.
Try checking the ground to the alt. by placing a temp. jumper between the alt. and the battery ground.
If the voltage at the battery now reads in the mid-12's then the ground/mounting of the alt. is dirty and causing the issue - clean the mounting bolts and re-tighten then correctly to assure good ground path to engine - also check the engine ground, I've found more than one problem caused by a broken or defective engine grounding path.
If the above does not give the correct voltage at idle, the brushes may be at the end of their life cycle or internal diodes in the unit may be starting to fail or are weak.
Check and replace the brushes as needed.
Check and replace the Diode Trio or the Rectifier Bridge will return the alt. charging function to normal.
The internal Regulator is the least likely to be causing this issue at idle at this point.
= this is why we love them for tractors and other off-road applications