My Kenmore electric dryer won't heat. What should I do first. It runs fine and tumbles but with no heat.

Are you comfortable using electrical tools? Do you have a multimeter?

If the answers to the above are "yes", then
1. check to be sure the heating element is not burned out. Disconnect one end of the heating element and using the multimeter on an ohm scale, check for continuity. If it's open (large reading on the meter), replace the heating element.

2. If the heating element is OK, reconnect the heating element and turn on the dryer. With the multimeter on an AC voltage scale (250 volt scale), check for power to the heating element. You should see approximately 240 volts AC across the heating element.

What you do after that depends on whether you have power and the heating element is OK, it should produce heat. If that heat isn't getting to the clothes, you probably have a plugged vent line -- not getting enough air through the dryer to take the moisture away from the clothes. If you do not have power, then you need to follow the circuit through the thermostats to make sure they are closing when the unit requires heat. You may also have a faulty switch in the control unit (timer or whaterver).