It is hot and my AC isn’t turning on. I bypassed the thermostat at the furnace, and the AC came on. How long can I leave the thermostat jumped? It is late and I can’t replace the thermostat until tomorrow night. I need to sleep and have the house a little cooler for my dogs throughout tomorrow. I plan on unjumping it before I leave the house in the AM.
If your AC unit was running correctly before the thermostat failed, then it will be OK to run it continuously until the AM when you plan to shut it off. Just don't freeze tonight because it won't be cycling on and off. When weather is extremely hot, AC units can run continuously and many do down here in South Florida. Just replace the thermostat as soon as possible.
Imagine you had a working thermostat and you flipped it to "A/C" and set the temperature to 50F. The thermostat would "call for cooling" so long as the temperature is above 50F. Since I bet your system would never get there, that means it would "call for cooling" continuously. That is fine. If your heat pump unit can't run continuously, then there should be protective circuit built into its internal controller.
So, the idea of "call for cooling" all night is legitimate.
To call for cooling, the thermostat shunts (i.e. shorts) (i.e. jumpers) terminals R and Y.
If you were to jumper R and Y yourself either at the thermostat or at the furnace, that would be the same thing.
The only difference is the furnace is full of Very Bad Things you must never, ever jumper to. Easy to make a mistake there and set something on fire. Whereas, at the thermostat you can't get in too much trouble. (worst thing you can jumper R to W and R to Y and call for both A/C and heat at once lol.)
Also, jumpering at the thermostat proves out the thermostat cable.