I guess it depends on the size of the rat but I'd say ~2-3 hours would ensure thawing. To be honest I didn't have any problems with smell at all. I actually leave it to thaw near the snake's enclosure to sorta pre-scent.
I imagine constant thawing/refreezing/thawing (in the event that the snake does not eat) would make things stink. But since your snake is a good eater, this shouldn't be an issue.
Like mentioned by another poster, what are the chances of the rat splitting if I put them in hot water after thawing?