What will happen if a temporary filling comes out of a tooth that has had a root canal?

A
root canal tooth that has been asymptomatic, that is, without pain for several
months, should not exhibit pain unless one of two things occurred. One is that the temporary filling has been
leaking and bacteria has re-infected the canal.
This would require re-treatment (another root canal in the same
tooth). Two is that, the fracture of the
tooth has extended into the floor of the pulp chamber in which case the tooth
may not be treatable. Since you did not
specify where the tooth is located, I will assume that it is a posterior tooth
and that the latter explanation is the most probable one, fracture through the
floor. However, it could be that the
filling is simply digging into the gums; I hope that this is the reason. Anyway, get to a dentist right away to
ascertain the real reason for the pain!
Good Luck!

I agree with the doctor answers below. It sounds like your tooth is now fractured. Temporary material is weak. Even if the tooth had a filling it could have fractured because the tooth becomes brittle after a root canal. 

Check with your dentist ASAP to check that tooth is not fractured or RCT is not failing. One of major reasons of RCT failure is lack of restoration after rct . 

Teeth that have root canals are much more prone to fracture--it is critical that they be restored appropriately soon after the root canal is completed--The danger is that the tooth can break or split where it must be removed--please see your dentist asap--because it has had a root canal it may not hurt like a tooth that has a live nerve in it. Also the space where the nerve was can soak up the bacteria from the oral cavity and the root canal would have to be redone. Please see your dentist soon. Kind Regards--Dr John Merrill