change the thermostat?

My Hotpoint elec oven works great, gets upto temp and cooks well...then suddenly for no reason everything turns off, stops working, no lights inside the oven or heat. (power is still on to the oven as the clock is working) The a few mins later, everything returns back to normal on the oven and it continues to cook.
Will this need a new thermostat or thermostat cut-out? Will it be the thermostaat with the long probe which goes into the oven itself?
Thank you.