Thermostat housing cracked and is leaking on a 2001 ford fous. How much would it be to fix this?

And can I possibly fix this temperoraly with duct tape or something?

It will cost you as much as a local shop will charge you and no, you can't fix it with duct tape

The thermostat housing is a square 'plastic' block that is bolted to the cylinder head. On the side where the block contracts the cylinder head, around the coolant hole, there's a groove machined into the 'plastic' that contains an O-ring, that seals that surface. When Ford machined the groove into the block, they got too close to the edge of the block, so the edge of the groove wall cracks-off & allows the O-ring to be pushed-out of the sealing surface, causing the leak. Just MAKE-SURE that the new 'plastic' block you buy has some meat all around the O-ring groove. When I fixed my girlfriend's '02, I had to buy the new block right from Ford…

Depends on if you carry out work or have garage do it. Housing itself and new seal is not expensive per se. If we have corrosion under seal? We may need re-machining or special sealer used to effect a proper leak free system. Though for very small leaks an internal leak sealer that mixes with coolant can be used.