The car is a 2001 Neon with a 3-speed auto tranny. The problem is poor
accelration at low speed  after the car has been driven for 20 miles
or so in hot weather.  The car runs fine at freeway speed, but it just
wouldn't accelerate at low speed, especially when driving uphill. It
feels as if it were in too high a gear, and I could detect a slight
"burning clutch" smell after driving up a steep hill.

I suspect the problem is in the transmission, but I want to be sure it
isn't engine related.  Is there any simple test I could do to
eliminate that possibility? Any ideas?

Nick