Is it normal for an 87 Grand National to surge at idle when warm?

Scan first, for sure. That check engine light is your friend here. You can ground the two pins in the diagnostic plug under the dash with a paperclip and the light will flash the codes at you, no tools needed. A cheap handheld reader for these old GM cars gives you live data too, and live data is where the answer usally hides.

Mine did almost exactly what you're describing years ago. Warm idle surge, nearly died at stops. Turned out the throttle position sensor had never been reset after some previous owner's intake work. There's a specific relearn procedure on these where you disconnect the idle speed motor, set the base idle, and let it relearn. Sounds like voodoo but these cars depend on it.

Check the fuel pressure regulator too. Pull the vacuum hose off it with the engine warm and look for raw gas in the line. Sitting cars love to rot that diaphragm, and a leaking one dumps fuel right into the manifold and wrecks the idle. Same story with the oxygen sensor. If it's original it's long past dead, and a lazy one makes the computer chase its tail at exactly the warm idle range you're describing. Your coolant temp sensor theory is legit. Compare what the computer thinks the temp is against an infrared thermometer pointed at the housing. Big mismatch means the computer never exits its cold fueling mode and warm running gets wierd.

Also pull the idle speed motor and clean it along with the throttle body passages. Old oil vapors gum those up badly on cars that sit.

On the numbers matching worry, sensors, plugs, wires and hoses are maintenace, not modification. Correct spec replacements don't hurt resale. Bag and tag every original part you take off and the next owner will thank you. Don't let a cheap sensor scare you off wrenching on your own car. Report back with whatever the flash codes say.

That barn-sit smell alone tells me the EGR is probably hung open a hair. Warm idle surge and a near-stall at a light is textbook EGR on these, and a stuck valve leaks in a way carb cleaner spray won't ever find. Old trick: let it idle warm, reach back there and tap the valve with a wrench handle. If the idle changes, there's your answer. Pull it and clean the carbon out of the pintle seat, plenty of them come back to life. I've also had good luck just driving one of these hard for a few heat cycles before diagnosing anything. They sit and get lazy.

Before anyone touches a sensor, go over the grounds with a fine tooth comb, becuase these cars are notorious for it. That battery cable to the block and the little strap to the body have been sitting in barn humidity since 2011 and a half volt of drop on the ECM ground will make a perfectly good computer behave like a haunted one. Clean them to bare metal, dielectric on top after, and retest. I chased a similar warm idle wander on my old T Type for two weekends before a multimeter pointed at the cable end that looked fine but was green underneath the clamp.

Not sure if anyone's said this yet but check under the hood for mouse damage. Mine sat in a shed for four years and the little furry jerks chewed through a couple of the thin wires going to the computer stuff. Ran weird in all kinds of ways til I found it. The insulation just looks fine from a distance, you have to bend the wires and look close. Also how does the rubber on the fuel lines up top look? Old gas smell plus barn air eats that stuff. Is there a nest or acorns anywhere under the intake on these?

That warm surge on mine ended up being the memcal contacts in the ECM. Car sat in a pole barn for six years and the little chip sockets get a green film on them that you'd never suspect. Pulled the cover off under the dash, popped the chip out, and a plain pencil eraser cleaned the legs right up. Car idled like new that same afternoon. Worth two minutes of your time before you buy a single sensor.