Why won't my Kenmore microwave model #721.63252301 heat?

If everything works, but the microwave oven does not heat, this is most commonly caused by a failed magnetron. The magnetron is essentially, the heart of the oven that produces the RF energy that is used to heat your food. In order to replace a defective magnetron, you will need to consider the following:

1. You will need to uninstall the oven from over the range in order to replace the part (you will need to do this anyway, if you decide to buy a replacement oven).
2. Ensure the oven is UNPLUGGED before servicing anything inside the cabinet and remove the exterior case in order to access the magnetron. There are several websites that you can use that illustrate how the oven is assembled:
searspartsdirect.com pcappliancerepair.com appliancepartspros.com
NOTE: If you've never repaired an appliance on your own before, a microwave oven is usually not a recommended appliance to start with. Some models can be rather involved in taking apart.
3, The magnetron replacement part number for the model you have listed is 6324W1A001H. The average cost is about $42. NOTE: This model also has a thermostat that if tripped, may also cause the same symptoms. The thermostat acts as a fuse if the oven cavity overheats. The part number is 6930WRT002F. You will need to remove the thermostat from the oven and take a resistance check across the component terminals to determine if it is good or not. A low resistance reading indicates a good thermostat. An infinite reading, indicates a blown thermostat and needs to be replaced. The average replacement cost is about $5.
Review the parts illustrations at the recommended websites to see if this is something that you may be able easily take apart and reassemble.
If you have any questions, please post back and let me know. I hope you find this information helpful.
CAUTION: DO NOT operate a microwave oven with the exterior cover off. The voltage inside the High Voltage network where the magnetron is installed can exceed 3,000 volts!