edit - what french G said.
Waterpumps usually fail at the bearing. Coolant weepage will show around the shaft and through any weep holes.
Check waterpump shaft bearing (on cold engine) as follows:
Remove Belt;
Grab waterpump pulley;
Wiggle (the pulley!!).
Any side to side play (lateral movement) of the shaft or pulley is a sign that the bearing is out or on its way. There may be additional coolant leakage at the limits of movement.
In and out play (axial to the shaft) is to be expected (up to 1/25 of an inch or so).
Check heater core -
Unhook hoses going into firewall.
Put garden hose on one spigot or hose going into the cabin.
Point the other hose (or add a length of hose to the spigot to avoid spraying yourself with coolant and sediment) to a proper receptacle.
If there is good flow, heater core is okay.
If you are very obsessive, feel free to flush core with distilled water.
Dispose of antifreeze and rinse water properly.
The same can be done with the radiator. Remove upper and lower hoses, open any drain cocks.
Put a wash tub at the lower opening.
Stick the garden hose in the top hose port (with a wet rag around the garden hose to seal it - you want all the pressure down through the radiator). Check your flow - it should be unrestricted.
Dispose of antifreeze and rinse water properly.
I agree with the probability of an air bubble or backwards thermostat. Before proceeding, it may be appropriate to confirm the installation (and heck, for 8 bucks, buy a new 'stat)
This is how I burb my cooling system.
Remove fill cap on cold radiator.
Start truck.
Have a bottle of antifreeze (mixed 50-50 with distilled water)
Turn on all the heaters
Warm up to operating temperature
Pull truck up on ramps (I've done this on a bumper stop in a parking lot, or a street curb) - the point is to elevate the front of the vehicle a bit. Set emergency brake (and chock wheels)
Climb up on front bumper and reach in and squeeze all of the hoses. Grab a hose with a gloved hand (motor is running and hot) and squeeze the hoses quickly and forcefully. The goal is to force a wall of water through the system and dislodge any clinging bubbles. Do this repeatedly. All hoses (heater hoses, upper and lower radiator hoses).
Hot coolant may splash out of the filler hole, this is okay. Keep the radiator filled to the top. Keep squeezing and filling, filling and squeezing.
Climb in the cab and see if the heat is coming out. Remember, if the t'stat is stuck closed, no heat will come out, and the heater hoses will not be as hot as the other hoses.
Good Luck.
