When things get hot there is too much current flowing. So the next question is WHY?
That motor is rated 2.4 amps at 2v. How much current do you think it might be drawing with a 12v supply? It is likely to far exceed the capacity of the shield and you are probably lucky the shield shuts down before the motor is damaged.
That motor needs to be driven by a proper stepper motor driver board that can control the maximum current in the motor coils. You might usefully read about the Pololu A4988 stepper driver board as the website has a lot of useful info. However the A4988 can't manage 2.4 amps. You should probably be searching Ebay for a driver that can handle 3 amps or more.
Alternatively get a motor that needs less current - but you should still use a proper stepper driver board.
the arduino motor shield uses the L298 driver IC, current can be upto 2A, but as tests, the driver IC would be very very hot when the driver Current >1.5A, a heatsink is Necessary?
by the way, you may need some other driver solution for drive such a large current , using the H-bridge circuit is a good idea. may the this H-bridge shield can be help:Dual Channel H-Bridge Motor Shield (8A 22V) Shield Arduino Compatible in elecrow store.
This low-impedance bipolar motor needs current-controlled drive from a chopper
driver, it is not suitable for simple H-bridge at all, even if you could find a 2V power
supply in the first place.(*)
The windings are 2.8A, 0.7 ohm. That's too much current for any single-chip
driver and a discrete chopper driver unit is needed, typically these are
sold as commercial microstepping stepper motor driver units.
(*) The max rotation speed depends on the supply voltage to the chopper drive
(anywhere from 24 to 100V is commonplace). An H-bridge from a 2V supply would
barely get 200 rpm from this motor.
I think someone else already mentioned that you need a chopper driver , not an L298 driver , which means you won't be controlling the four input pins directly like using four digital signals like you would with an L293 or L298 driver. Instead, you will simply connect the motor winding to the output pins of the chopper driver and give it a STEP pulse and a direction HIGH or LOW on the DIR pin. Using only those two pins , or those PLUS an ENABLE (some people hardwire the enable because they don't need to switch it off and on) , you will control the stepper with only two signals (+ Enable). Some drivers also have microstepping capability and those three input lines can be hard-wired or digitally controlled as well. Any code that was written for an L293 or L298 will not work with a chopper. You will have to look for chopper driver code that defines a STEP pin and a DIR pin and use that code. (or you can ask us and we can post an example sketch that can give you something to start with)