The intent of the temp switch is to not circulate cool or cold air. So when the minimum temperature is reached, the switch closes, the fan runs... but it cools down the stove body, so the temp switch then opens... it's too cool for the fan.'
Youo might be able to put a rheostat on the fan motor, but only if it is the type of motor that will accept a reduced voltage, otherwise the rheostat will burn up the motor [overheat, melt insulation on windings, short internally, motor dies]
You can try putting a duct to the inlet of the fan and ducting warmer return air to the fan. This way it will not cool the stove box so fast, and the output heated air will be warmer.
Hope this helps.