What year? It's going to matter...
"Open Loop" is the warmup mode, before the HEGO sensor reaches operating temperature and reports on the fuel mixture and starts to affect fuel trim.
"Closed Loop" is the normal operating mode - when the HEGO is at operating temperature and can report on the presence/absence/amount of oxygen in the exhaust gas stream.
Note that neither of these modes has anything at all do to with engine coolant temperature!
"Limp Home" is the operating mode reserved for a major failure - performance suffers, fuel economy and efficiency both suffer - but it will (hopefully) get you home.
The thermostat governs whether the engine gets into "normal running" mode from "warmup" mode, using the engine coolant temperature as reported by the ECT sensor. Again, this is a separate system from the HEGO sensor. This distinction is important - it is possible for the engine to be able to run in "Closed Loop" but still be in "Warm Up" mode! "Open Loop" operation is typically one minute or less with a HEGO sensor, while "Warm Up" mode typically runs five minutes or so.
With pre-OBD engines, it's possible to pull the operating temperature down significantly without ill effects. I've pulled the op temp on my 88 down to about 185-190*F; fuel economy increased slightly, emissions decreased slightly (I've got the air police reports to prove it. Somewhere...) and I'm sure there is a salutary effect on coolant and engine oil life as well. However, the XJ was classed as "pre-OBD" until the end of the 1990 model year, when ChryCo stuck their SBEC/SMEC OBD-I system in in place of the RENIX.
OBDI and OBD-II both monitor engine coolant temperature, and will "throw a code" if it's out of range for too long. You can probably get away with depressing the operating temperature about 5-10* on an OBD-I (1991-1995) rig, but that's about it. I wouldn't even bother with OBD-II.
Bear in mind also that a thermostat does precisely two things:
1) Prevents coolant circulation through the radiator until a predetermined temperature is reached (typically 160*, 180*, or 192-195*F.)
2) Acts as a "flow restrictor" when open to allow more time for heat to transfer into and out of the coolant.
Neither has anything to do with the actual temperature at which your engine runs - that's governed by other factors. However, the thermostat does help to reduce warmup times, by allowing the coolant in the engine block to stay in the engine block until it gets warmed up. There is usually a detectable drop when the thermostat opens (and the hot coolant volume gets mixed with a similar volume of "cold coolant,") but this recovers rather more quickly than when the engine is warming up.
Mechanically and chemically, there is no good reason why we have to keep the 210-215*F operating temperature - however, OBD will throw fits, and this could cause you to fail inspection...
HEGO = Heated Exhaust Gas Oxygen (sensor)
ECT = Engine Coolant Temperature (sensor)
OBD = OnBoard Diagnostics. Currently in its second generation (as of the 1996 model year on most vehicles)
SBEC = Single Board Engine Controller
SMEC = Single Module Engine Controller. Also called PCM (Powertrain Control Module,) this usually integrates the transmission controller and engine controller into a single module.
RENIX = RENault/bendIX control system, used in 1990 and earlier XJ w/AMC engine and fuel injection.