Water pumps don't go bad, either the shaft seal fails (anti-freeze will leak around the shaft) or the impeller breaks (will make noise). Could be the thermostat but if you have trapped air on the bleed screw side of the thermostat it may not get hot enough to open. Make sure you get most of the air out so you have a pretty good stream of fluid coming out. If the lower hose stays cold change the thermostat.
