If the battery is getting hot, it is being overworked. This can be because the motor is demanding too much current, or because a wiring error has put a short on it. A shorted battery will certainly get hot, whether it gets hot enough to rupture is another question, 1st question is "what kind of battery?". If its a PP3, (guess, that being the commonest 9 volt battery using that kind of connector) it probably won't have enough power to harm its surroundings, but equally, it won't have the guts to drive a motor, either.
Find a battery of the same voltage as the motor rating, use that. 2 of AA probably the best bet.
Take the wires that you show going from the battery -ve away from the switch altogether.
Take ONE of the microswitch + wires and connect it to the terminal currently shown unused.
Looking back at the picture, the switch IS shorting the battery when the contacts make. This ensures that 1- the battery gets hot 2- there is probably going to be no power left for the motor when it is wanted. 3- that motor probably wants more current than the battery can supply. This means that much of the energy in the battery will go into heating the battery.