NO. Bypass the heater core by connecting the Inlet & Outlet hoses going to the heater core together. Do not plug either hose.
yes the heater core can be bypassed by connecting the heater hoses together
No
NO! THE HEATER CORE IS YOUR CARS HEAT SOURCE YOU CAN BYPASS BUT IS NOT A GOOD IDEAL IN WINTER!
How do you replace a heater core in a 1998 Ford Expedition?"
That means either you have air in your heater core or your heater core is being bypassed
If the heat is on that would explain it. But if you are running the air conditioning, the compressor is on and fully charged with r134 it is probably the air mix door inside the heater stuck in heat mode.
you may have restricted the flow or something, depending on how you bypassed it. I have bypassed my 96' s-10 and have not noticed any temp. increase. It doesn't act like a radiator until you actually have the heat on so it shouldn't affect the temp anyways. So for a fix I would say replace the heater core, or make sure you don't have any restrictions where you bypassed it.
How do you replace a heater core in a 1998 ford expedition?"
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it shouldn't
I am guessing you are talking about a car's HVAC system. If so, yes it will still work as the heating for your car comes from a heating coil fed from your engine coolant. There is a separate cooling coil fed from the AC system.