2001 Lincoln Navigator, the heat blower stops working when accelerating!

starter bendix is probably bad or it has stripped teeth on the flywheel. the acceleration problem sounds like you were in limp mode

Check thermostat

Your fluid in the unit is too heavy and will act this way until it's warm enough to start flowing thru the pump. Heat from the engine is apparently what is warming the fluid enough to make it work after it warms up. Have the fluid changed to a much lighter fluid in the pump reservoir.

It sounds as if you have a broken vacume line under your dash that controls the flap inside your heater box

Since your blower is working and it is a heat issue,thats where we'll start,First thing is have you checked the coolant level in the radiator when engine is cold,make sure it is filled to top,next verify you have coolant in reserve ,Start your van and get it up to normal operation temperature,If your heat gauge on the dash works correctly it should be 190 degrees,Now lift the hood and locate the two heater hoses going into the heater assembly at the fire wall,Both hoses should be hot to hold on to,if both are hot and no heat inside your problem will be the blend air door in heater assembly.
if neither hose is that hot you need to replace the thermostat in the engine to get it up to 195 degrees.
if one hose is hot and one is luke warm then the heater core is blocked and to blame. hope this helps you.

Check for a vacuum leak. WHERE is the magic question.

check to make sure heat flaps are opened,check fuses for blower motor or check blower motor

damper in duct to change air flow from heat to air is not working most probably. I am almost certain the navigator will have an actuator motor that has stripped, or the motor has gone bad this is constantly working when you use climate control to control air temperature.

Look in your owners manual..it'll tell you the capacity for your cooling system..add a 50/50 mixture of anti freeze.....the no heat problem may be that you need a new thermostadt.