Starter on 5000S?

[Thom Jones]

Before I go through the herculean task of replacing the starter in my
'88 5000S, I thought I'd ask and see if the symptom really fit my
proposed 'cure'.
The car almost always starts fine when cold (and when I have enough
cca in the battery).  But let it warm up a bit whether from the engine
running or from the 90 degree temps outside and the starter motor just
spins without turning over the engine.  Sometimes the starter will
catch for a second or two but then disengages and just spins again.
Sure sounds like the starter to me, but before I spend the $200 and
the hours of work, I thought I'd ask for a concurring opinion.
Thanks for any insight!