87 3.2 stumbles when temp is cold
 

Warm weather finally, and my 87 runs great, but when if was colder, say under 60 degrees F, the car would stumble with anything less than the most gentle throttle and cut out occasionally.
Is there an outside temp sensor in the FI system? Any other ideas?

when was the last time you changed the fuel filter, it could be fuel starvation at low throttle.

Try some BG44K, it will clean the FI system and the fuel filter too of and soluable debris.

Or Bring her up to temps and do an Italian Tune up to get rid of some of the carbon deposits

Don't think thats it- Relatively new fuel filter, new engine relay, and it runs like a top to redline in all gears now that its warm out.
When its cold, cuts out, as if the mixture was too rich or the distributor was broken.

Well, when she heats up materials expand. put the car at TDC and remove the dizzy then test for slop horizontally if there is axial play you need to find another one, if only horizontal play you can add some stainless steel shim to take up the play.

While you are there check the base idle by jumpering B&C in the engine bay.

Cylinder Head Temp sensor. CHT. A search will turn up days worth of reading. -J

Check the OHMs, nice one JAR0023 SmileWavy

Lean stumble, vacuum leak. Lots of vacuum hoses on these intakes and intake gasket/insulators are known to degrade.

A simple spray of a volatile liquid around these areas should find your issue...hopefully. If there's a leak, the engine RPM will raise.

Be careful with starter fluid since it corrodes metal from my experience not to mention fire risk.