Bias thermostats with 4 terminals...the lower terminals must have continuity for the dryer to heat. The 2 terminals on the upper half of this stat are a small heater coil which makes the thermostat get hot quickly to simuate a certain temp. The upper wires are connected to the heat selector switch above and send 240 volts thru the thermostat heater when needed. You are only concerned with the lower large terminals showing continuity.
Have you checked continuity thru the element?