You need a "comparator" for this.
Transistors like the 2N22222 don't turn on because of a voltage, they turn on because of current. Trying to manually tune a circuit to turn on at a specific voltage is doomed to failure.
Connect the output of the comparator to the base of your transistor. Connect one input to your temperature sensor. Connect the other input to a potentiometer and you can dial the temperature where the comparator triggers.