It is a 10 guage wire. If i connected the wire to a 240v switch in the house
could i replace the box on the garage without having to put in a thicker wire?


Possibly. You will need four conductors unless the sauna does not require a neutral. The other end will need to be connected to a two pole 30 amp circuit breaker. You will need a grounding conductor. You will also need to follow the manufacturer's installation instructions in addition to the National Electrical Code and local codes.

I am assuming that the existing circuits in that fuse box are no longer in use.

John Grabowski
http://www.MrElectrician.TV