From what I can gather, you are after a cheap solution, what I have done at home to try and solve the same problem might give you some ideas:

1. Fire proof safe - (1hr seems to be the base level at hardware stores, depending on budget I'm sure longer times available)
2. drill hole through safe for the power and network cable. (make as small as possible - cut power cord and fit plug afterwards)
3. Fit fire rated collars on both inside and outside of hole. Use fire rated sealant to make sure airtight. (the fire collars crimp the cables when exposed to heat and will seal up the hole)

This will give you an enclosure that will resist fire heat for about an hour. Cleaver placement of the safe will likely give you longer time to get the fire out / retrieve the hard drives. (Away from flammable material/usual fire sources; fuel & chemical storage, power switch boards & under a sprinkler would be handy)

Note: The 1 issue I currently have is heat build up inside the safe, 1 solution I have yet to try is to make the safe a lot bigger than the NAS unit as to give more surface area for the heat to dissipate out, 2nd idea is to purchase newer NAS unit with the hope that it is more energy efficient

I hope these ideas help.

Cheers,

John