Pull the range away from the wall. Turn off the gas supply valve to the range by turning the knob on the gas line clockwise. Unplug the power cord for the back panel from the electrical outlet, if one is present on your particular Kenmore range.
Remove the grates from the top of each stove burner and set them aside. Raise the top of the range by grasping the sides of the top and lifting it. Prop the top open with the prop rod. Remove the adjustment knob from the thermostat assembly by pulling it straight off.
Remove the retaining bolts from the thermostat using an adjustable wrench. Remove the thermostat from the gas manifold by pulling it apart. Remove and discard the gasket between the thermostat and the gas manifold.
Place a new gasket on the gas manifold. Install the new thermostat and tighten the retaining bolts with an adjustable wrench. Place the adjustment knob on the thermostat assembly by pushing it firmly onto the stem at the front of the Kenmore range.
Plug in the electrical cord for the stove, if one is present on your Kenmore gas range. Turn the gas supply valve on at the gas line by turning the knob counterclockwise to open it. Push the stove against the wall. Light the pilots on the Kenmore stove unless they have an electronic ignition module.
Turn the oven on and set it to the lowest temperature setting on the adjustment knob. Place a metal food thermometer in the oven to test that the new thermostat is operating properly.