2000 Mercury Marquis runs rugh untill it warms up

OK I would unplug the temp sensor and ohm it when it is cold and get back to me with the ohms and the air temp at the time you check it. Now on the guage unplug the single wire to the temp sending unit for the guage and with key on engine off gound it out does the temp guage peg? If so replace the sending unit. Let me know what you find.

i discovered the intake is cracked where the heater hose goes into the intake atthe spout that may be the root of all the evil thanks jeff

Yes it can be and this is available at most parts stores if you want to do this yourself. Let me know how it goes.