Your going to find some folks here that will say "yes", just give them some eggs. I personally don't use it or recommend it. They will be raising an "emergency" queen. At that point, they don't tend to be too fussy about the age of the egg they use, they just need a queen. Sometimes it works, sometimes it doesn't. With this method, your "sometimes it doesn't" chances are higher. Furthermore, by the time they raise a queen and she mates, you are looking at upwards to a month and a half that brood rearing will be halted. You will definately be hurting your colony this way, and potentially really setting them back if a queen does not work out.
Personally I think you are risking a lot for a $10-15 investment in a quality queen.
You can certainly try raising queens from you calm hives, but don't put you hot hives in jeopardy until your new queens are laying and can take the place of your older queens.
Any time you make a queen-right colony queenless, you are risking their future.