Blend Door Problem
Your problem sounds like the common blend door problem on the Ford Expeditions, and Ford Explorer. The door is on a vertical axis and when it breaks, it can swing back and forth randomly giving heat or AC or nothing. The difference on acceleration is the force placed on the door swinging it one direction.
You can check the operation by fully opening the glove box, removing the actuator motor on top of the plenum box and examining the blend door axle (the actuator is under the unit on top of the hump behind the flexible black plastic cover. It is on top of the unit, behind the glove box in the 2002 F-350 though). Pictures of the common fail signature are available on the Related Links below. There are several "free" fixes that mostly are worth what you pay for them. The solution on the web site is solid and proven over hundreds of vehicles and will resolve the problem once and for all.
you may not have the heater water hoses plugged in
The heater might blow cold air in a 2000 Silverado because the thermostat is sticking and not changing from cold to heat. The thermostat is usually located in a hose that leads from the radiator to the motor.
One of the reasons a 2000 Jeep Cherokee heater would randomly blow cold air and then hot air and then cold might be that there is a problem with the hot/cold duct. The air or a vent might be inadvertently blowing periodically.
Low coolant? Bad thermostat? Heater core plugged, restricted or airbound? Bad heater control? Water pump not circulating coolant?
Your heater will blow cold air only.
Probably your thermostat
check you antifreze level if it is low you wont have eat or if you get lots of fog your heater core is bad
It doesn't really blow it out it just warms the cold air.
The temperature blend door may be at fault.
It is either your water pump or your thermostat
you need to replace your heater core
it wont blow heat itll blow cold air