I have an '88 Isuzu Trooper with a 2.6Liter 4 cylinder engine and when the engine is cold and I drive it for about 4 or 5 minutes, the temperature gauge nearly points to the "H" position before it starts going down to normal pointing straight up at the very center between "C" and "H".

Is this a sign of a weak thermostat or is this just normal for a 4 cyinder engine?

Has the water pump been replaced?

No, I haven't replaced the water pump in the 6 years I had it. But how can the water pump be bad? After the thermostat kicks in, the temperature returns to normal and stays that way down the road.

By virtue of the fact that it cools down at a certain point, the thermostat is opening, eventually. Try a thermostat first, but I ended up having to replace the WP. My overheating was being caused by lack of sufficient circulation due to a shot pump and exhibited the same symptoms.

Yes it is a weak water pump. Also replace the thermostat and flush the entire system when you do it.