As Endlessness said, I hope that this fridge is just for extractions. As that stuff evaps it will soak into any food that is in the fridge. Please be safe.

Yes and no. You're right that the naphtha hydrocarbons are volatile and should evaporate cleanly on their own, so letting it stand (or breaking it up and moving it once in a while) will dry it up well.. BUT... This doesnt take in account that as crystals are formed, they can trap solvent inside their crystal lattices, so to redissolve in ethanol/acetone and re-evap will remove those small naphtha traces.

The OP should make sure that his naphtha evaporates cleanly in the first place, in any case...