It should be cold water - but you could use room temp water to quicken the process, not warm though. Just make sure to take the bird out as soon as it is no longer frozen- also, I would recommend allowing the water to circulate inside and out - just dry the bird very well before cooking it.
I found this advice online:
If you're in a hurry you can use this method. Leave the turkey in its original bag, put it in the sink, and cover it completely with COLD water. Either leave the water running slowly or change it every half hour. This method takes about 30 minutes per pound, or 6-9 hours for an average size turkey.
If your turkey is partially thawed, maybe you can do this. I've also filled the cavity with running warm water to help get the ice out of the insides.
I found the recommendations on my frozen turkey, one day in the fridge per 7 pounds of bird, were useless. Ended up leaving it out on the counter all day yesterday. The bird was still quite cold to the touch but not frozen. Yeah, I know you're not supposed to to do this but I figure it's how my mom always did it and no one ever got sick.
In my opinion, your only option is to immerse the turkey in bucket with warm water, making sure the water is filled into the cavity of the bird and you must chance the water frequently until the flesh is soft.
FWIW, this is a dirty little secret how commercial kitchens defrost chicken breasts or parts in a pinch.