I have a Kenmore Elite Dryer (Heavy Duty) Model 110.62062100 which runs but produces no heat. Thinking it is a Thermal Cutoff problem, I went ahead to change that but no luck. I had the continuity of the heating element checked at the local Sears store and it came out fine.

Any idea what else I can do?

See this web site at Sears.com.
http://www.searspartsdirect.com/partsdirect/part-model/Kenmore-Parts/Dryer-Parts/Model-11062062100/0582/0151200/P0101065/00003?blt=06&prst=0&shdMod=11062062100

See bulkhead breakdown.

Could be part 42, 47 or 48

Use a meter and trace the circuit with it unplugged to see where the break in continuity is located. It's the only way. If you are just going to change parts you might as well buy a new drier. DrTom4444

Be certain that you have 240 volts available. Check your circuit breaker and also check the pigtail connections if you don't have a volt/ohmeter. A dryer runs on 120 volts, but to heat, must have 240 volts.