An F10 error on a Kenmore stove indicates that the temperature conditions in the oven are incorrect. Using a flashlight and a digital multimeter, you can find out what the problem is in less than an hour.
Reset the control board
Reset the stove's control board by unplugging the range, waiting one minute, then plugging it back in and turning it on again. This particular error can be resolved this way in some cases.
Inspect the oven visually
Use a flashlight to see whether the heating elements are physically damaged. You might notice a broken heating element or blistering on the surface of the elements. If this is the case, you need to have the heating elements replaced.
Check the heating elements using a multimeter
Remove the stove's rear panel and disconnect the heating element wires. Touch one of the digital multimeter probes to the left terminal of the heating element and the other probe to the right terminal. If you see a reading of up to 50 ohms of resistance, the heating element is fine. A reading of 0 ohms suggests that the heating element needs to be replaced.
Test the temperature sensor
Disconnect the wires of the temperature sensor, which is located between the upper baking element prongs. Touch the multimeter probes to the sensor terminals. A reading between 1,000 and 1,100 ohms suggests that the sensor is working. If the reading is above 2,500 ohms, the sensor is broken and should be replaced.