Look for a partially clogged vent or duct. It needs to be clear from the dryer all the way to the outside of the house.

Long time ago I had the same problem on a Roper Dryer. First thing I did was to take the back off the console then lift and roll it forward on a towel to get better access to the back of the timer. With the power disconnected I unplugged the two brown wires that go from the timer motor to the timer. I used a pair of jumpers and a lamp cord to power the timer motor directly with 110v. I have bad hearing and so used a stethoscope but you shouldn't need one to tell if it's running.

Next thing I did was to set the timer on a certain place in the auto dry cycle; left to go make a pot of coffee came back and it had advanced to near the end so I waited for it to cut off. Then repeated on the timed dry.. same thing.

Ok so I realized it wasn't getting power. If I remember right my timer was powered by the small orange wire that connects to the thermal fuse at the heater element connection. Some replacement kits for those thermals come with a smaller "push on" terminal which replaces the original and slightly larger, factory push on. Someone had done the job in the past and made a bad crimp which worked until a little oxidation finally did in the connection. A drop of Marvel Mystery oil on a q-tip and a re-crimp and worked like new.

Of course I suppose looking back it would have been more efficient to have tested the orange wire where it connects to the timer. I might even then red oil with a q tip and wiggle all the terminals on the timer with needle nose to insure contact.
But if you directly charge the timer motor itself and it doesn't run, well probably the timer.

There are a lot of timer numbers for Whirlpool Dryers and I don't know if they are all powered alike. Don't remember a Roper that isn't. Worth a look, I've seen it a couple times since.. Could be a blown element killing the power to the timer, but yours is heating isn't it:confused:

What kind of dryer is it?:confused: