A duff stat won't lose water, as it is totally sealed, the water pumps are a pain in the rs on these, I do one every belt change(3 years) whether it needs it or not, they're hopeless don't last very well at all.
Another thing to check is the heater matrix, check to see if the carpets are wet.
If the pump is leaking when bad enough it leaks at the seal/bearings itself that the impellor shaft runs in, this washes away the grease in the bearings, resulting in the ball races being worn away from metal to metal contact, and disaster if not caught early enough, you get a loud rumbling noise first, simply take off fan/alternator belt to eliminate that as cause.
Usually though it is the rear seal on the pump that leaks, and causes a dribble that lands on the ground just below the crank pulley.
tabetha