Heat is not getting heat - 1998 Ford Expedition

"Both" what heat up? Both heated seats? If so, the heated seats are heated using electrical current. The cabin heat from the vents is heated from engine coolant. The car will need to be running several minutes before heat will start blowing from the vents. If once the engine temperature gauge gets up to normal you still are not getting heat from the vents and are certain you have the climate control settings correct to be requesting heat, you probably either have a blend door issue or an issue with the valve that allows coolant to circulate through the heater core. I'm assuming that your blower motor is working and you can feel air flow, just the air flow is not warm. If you are not getting air flow, then the blower speed controller may have failed, the blower motor may have failed, or some other issue is preventing power from getting to the blower motor.

Most likely the Blend Door Acuatetor

Have you tried operating heat on recirc mode?

The heating coil is probably getting plugged up. You may have heat at idle or slow speeds, but once you get going, there is not enough coolant going through it to stay warm. Get the system flushed or replace the heating coil.

Verify whether the two tubes at firewall are getting hot, or one or the other is cold, or both are cold.
If the tubes don't get hot, then you won't get heat. If they are getting hot and you don't have heat, it's likely that the blend door actuator is not working properly to get heat from the heater core to the interior of the vehicle.

check the coolant level, if your blow motor works and your not getting heat the coolant is probably empty, the heat work when the engine gets hot and coolant starts to get hot, from there the blower, blows the excess heat into your car, low or no coolant means no heat

are the water pipes leading to the heatrer rad getting hot ??

all you could do is remove the thermostat to get heat in side it will just take longer to get heat

try replacing the heating core mine is the same way and that is what's wrong with it

due to the fact there is duel zone heating in these cars there is a heater control unit could a amplifier these tend to fail and you wont be able to get any heat a genuine unit is very expensive around $1500 but if you shop around you can get one for around $250 non genuine
then its just a matter of getting a jag tech to fit it

good luck