Mine went out on me at the start of spring, barely putting out any voltage, an VERY hot to the touch compared to the block, telling me it had shorted windings... .
Out it went, in with the new, and it's fine... .
If it were as warm or cooler than the engine, I would then assume open diodes or bad brushes, meaning a rebuild would work... or and open fuse (but rare unless you've been abusing your electrical system - or corrosion) but it's not how all alternators fail.
Windings do short, and when they do, the alternator can get hot and have low or no output.