For the last 2 night my furnace quit working. In the morning I took off the cover and put it back on and it started up. This morning I flipped the on/off switch on the furnace and it started up. Could it be the thermostat or is it something else?

Would help to know what kind of furnace. You may have a limit or roll-out switch open and when you open door or turn switch off and on you are resetting the switch and it will come on and run till whatever is causing it to lose power to happen again, so again tell us what kind of equipment you have
And anymore info you can find out