My son was playing video games in his room with a light on. He turned on a space heater and after I turned it off the power to his room went out. We could not find a breaker to that room. Is it a fire hazard since we can't be sure the breaker is off?

There is most likely a loose wire connection at one of the receptacles that needs to be found and repaired.

It should not be a fire hazard, however, there is always a slim chance. I can never say never.

An electrician needs to come in and find the loose connection, unless you have some knowledge of how to locate and repair the problem.