why the heater wont get hot
okay....the thermostat is stuck open...hopefully you've had a coolant flush as this will fail if the coolant is old and mucky~...so get new 50/50 mix and a new thermostat~https://www.google.com/#q=2004+Mercury+Grand+Marquis+ther mostat&tbm=shop&spd=3176755226586382219
Don't buy the 50/50 mix! A couple bucks more you can buy straight anti-freese and have 2 gallons of 50/50 mix. In stead of one gallon for a couple bucks more
50/50 mix is 50% anti freeze and 50% water why not buy straight anti freeze and mix it your self? You will twice the amount for your money
if both heater hoses are hot its inside the car diverter flap, if one is hot its the clogged core, if both mild its the stat
if the thermostat was stuck a code would be set and the check engine light would come on. most likely have a bad temp blend door actuator as stated by jimmy. very common on these and vary hard to get to. dash has to come out.
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