I've got a similar issue with the vx i just bought. It misses inbetween 1300-2700 at light throttle. a second after you get on the gas the engine feels like it changes modes and then pulls strongly and smoothly. I just put in the correct spark plugs (replaced the bosch with the ngk v-power), and hopefully that will solve the problem. I don't know enough about the engine coolant temp sensor to answer your Q. Hope you figure it out!
Getting a similar thing now with my 93 CA VX.... after I patched in a lean burn 49-state ECU and 5-wire O2. I can tell that it is going into lean burn, but then the injectors seem like they are randomly miss firing.... researching now.... thinking lean burn calibration of some sort.
I think a slight hesitation or stumble is a pretty normal characteristic of lean burn. But it should be very slight, and it should only happen at low rpm, and with light throttle. If you set up a lean burn monitor it's easier to follow the pattern of when this is happening.
There's also a lot of very good troubleshooting info in this thread, so you should go through the basic things mentioned. Check the timing.
One thing not mentioned above is valve clearance. It's probably not causing your symptom, but it might be a good idea to do it anyway.
Also, is your car CA or Federal? I assume the latter. How old is your O2 sensor?
I don't know much about Honda's, but I had a simular problem on a Ford Escort and it was the idle speed control motor. I think I would replace all the vacuum lines anyway since it can be done for just a few dollars, there could be small cracks in them causing the engine to surge. If it is not your problem now at least you wouldn't likely have to worry about a vacuum leak again for several years.
Edit: I just read another forum about the same problem on a Honda surging between 1000-2000 rpm it was his throddle body gasket. Might want to check that.
Just replace the sensor. It's very common and very easy. That same sensor can be found at the junkyard across many Hondas and Acuras. Just make sure you replace the correct sensor as there is more than one coolant sensor.
Whenever I buy a 15 year old Honda or Acura (I'm on my fourth), I just swap out the motor for a low mileage JDM replacement. It's cheap insurance and pretty easy. When I do this I also replace all the hoses, water pump, thermostat, timing belt, accessory belts, and anything else that is hard to get to once the engine is in.
You can spend a lot of time and money chasing down a problem only to find it's a blown headgasket, worn piston rings, or burned valve. Most likely you just have a vacuum leak but what will you have 20,000 miles from now?
Troy used to give me hell similar to what was described earlier in this thread. After having old gas in it, he wouldn't run worth a damn. You could be driving down the road just fine, then all the sudden it would stop getting gas, the RPMs would go all over the place, and sometimes it would sputter to a stall.
Replaced a dirty fuel filter. It didn't work. Then we cleaned out the fuel pump. That cleared it up for a couple of days. But then it did it again another day. Turns out the gas tank was rusting, and bits of rust were flowing into the fuel filter clogging it up, and keeping gas from getting to the engine.
After my dad swapped gas tanks from another Galant we had, it drove great and has never given me another problem since. All I've had to replace since that time was a leaky radiator hose.