97 Taurus overheating

Just purchased a 97 taurus 3.0 6c DOHC. Car overheats with in 12 blocks from cold start. Had 2 shops check out but neither knows. Dash says low coolant and service engine light comes on occasionally. Waterpump is good thermosat is good no leaks in lines or radiadtor. Radiator doesn't appear to be blocked. after putting in 3/4 gal of coolant and running it for 12 blocks it cools down and needs another 3/4 gal. again and again. Where is the coolant going?. Oil is good and clear no engine knocking or anything telling me its a head or head gasket please help

is there white smoke from the exhaust?

if there is, your head gaskets gone and your cylinders and burning/steaming the coolant. if it's not that, there's a leak somewhere.

No white smoke. Engine is very smooth sounding no mix of water in the oil both mechanics agreed that they both think there is no internal problem with the head or head gaskets.

how do you know the t-stat is good?

fans come on when they should?

you've removed the water pump and inspected it?

tested the radiator cap? Or just replace it.

Radiator is flowing well? Tested?

2 different shops....what did they do, just stare at it? they should have at least done a pressure test on the cooling system, pulled the plugs and looked at them and I usually pull one of the valve covers and look for sludge coolant contamination. Did they look at the trans fluid for contamination? A compression test or better yet a leakdown test needs to be done.

if you were burning 3/4 of a gallon of coolant in 12 blocks, you would have such a large white cloud coming out of the exhaust, you wouldn't be able to see 5 feet infront of you

Either some of the info isn't accurate, or you have a very odd deal.

3/4 of a gallon every 12 blocks? that didnt register when I read it, yeah they should be trailing a cloud. still 2 mechanics should have found something.

I took the thermastat out and it still overheats. no steam out of the tailpipe when its running. Both mechanics said the waterpump is fine but Ive lost confidence. How wold one check a waterpump?

It has a new rad cap. Pressure tested fine. both fans come on. i don't think they went as far as to pull the valve cover but sounds like I may need to
thanks

for humors sake, I'd pull the waterpump and check the impellor. Many cars these days use plastic impellors, and sometimes they shatter. What you're discribing, it very well could be that

waterpumps are actually not hard to change.
the actual process is simple. un bolt it and put another one on.
the hard part is gettign to the pump, as it is ususally buried under 3-4 layers of accessories on the front of the engine.