Honda Repair: 1992 Honda Accord EX Over Heating, radiator cap, honda accord ex

Question
So here it is. My 92 Honda Accord is over heating when driven.In Idle it does not. We found the smaller of the two fans wasn't running. We found the relay bad. The fan works. We have changed the radiator cap. All we did before this problem started was change all engine mounts and axle shafts. Is there any sensors we are missing? Once the car is warmed up. And we drive 1000 feet,  it goes steadily to the H on the dash and almost red. I need this car running. What do you suggest. All we can think of is the thermostat. Could this cause this problem?

Answer
a number of things.
-a thermostat only partially opening.
-air in the system
-a headgasket (the heat can be handled by the coolant at idle, but added power/heat from driving it cant)
-a water pump with rusted vanes (rare)
-maybe something else im not thinking of

i won't commit to anything over the net on overheating as that can cost people an engine.