1996 Lincoln Continental

First thought would be thermostat, but the chance of two replacement stats being bad is almost "nill". It sounds like you have covered most of the common causes of the problem. The next step I would recomend is having the cooling system checked for exhaust gases leaking into the cooling system. This condition will create air pockets in the system and won't allow the coolant to dissipate the heat from the engine block. There are kits available at most parts stores that will detect the presence of exhaust in the coolant. The most common cause of the problem is a bad head gasket or a cracked head. With close to 200K on the engine, I would suspect a gasket failure. Let me know what you find, or if I can help you further.