I have a 1995 grand caravan se. i live in mn. Heater will be used soon. The problem is when driving down the road the blower fan throws out the heat. but if you were to push the gas down to go faster such as getting to speed leaving town or to go against the wind the heat switch's from vent to defrost untill back to normal speed then heat comes back out the vent is this normal? my 1990 caravan did the same thing. Is this problem fixable?

Need to remove fan and test it on a bench by connecting it directly to a car battery. Removing items like this buried in the dash takes a long time, and its tricky to put back together.

If the problem is a lack of air flow from the vents, and you suspect the blower motor is not running at times, you would need to test the blower relay and blower motor for power and ground when it is not working.

Yes . Your heater is actually not an Electrical Heater or a Separate Heating system . Actually if uses the same Radiator Line . When Radiator is heated up it is cooled down with radiator Fan and coolant . But when you use the heater function , this hot fluid is passed through a heating coil tube and blower fan is used to take that heat inside the car .
So I think now you understand , why you are not heated up in a short run . You really need to make the Engine + Radiator Warmer ( that is natuarlly happened when you run more) to get Warm air inside.
Please rate my answer fairly and Support me With Regards and Season's Greetings Deepak Richard

Does the fan work on A/C? If the fan isn't blowing, check the fuse. Heat when going down the road is simply an indication that the air from outside is coming through the system. If fuse is fine, blower motor is probably out.

If the blower was working why did you replace it?
Heat is made by the engine, and then it is sent into the heater core and a fan, blower motor, blows heat into the car.
First - check that the coolant level is full. If not add MIXED coolant.
Then drive a few miles for the engine to get hot.

If coolant level is full, the thermostat might be bad, or the heater core might be plugged.

take out the blower motor
if the bearing is ok

use a vacuum cleaner to suck out the debris in the piping

Pretty sure I have answered this about a million times. Blower motor is on engine side of firewall on passenger side. You can run a hot lead to it to check if it's working! You did check fuse... Right?

sounds like you have a wire that has lost or burned off its cover and is grounding out the vehicle and has soon as its power is cut the wire breaks free from the bare metal and thats why you can immediatly start the vehicle

check the coolant level, I had the same problem low coolant level.....no hot water to the the heater coil.

vacume line take the front off the dash so it want get the way. look at all line theres a valve looks like a flat round disk if it dont work than throw it . plus your fan has 3 to 5 stages on the moter like low med hight