RPM when idle odd, Spark Plugs?

[Cubejam]

Noticed an odd occurrence in my 2010 120 vti when the car is at idle.

Sitting the car will start & idle at around 1000rpm. When warm the engine will idle around 700rpm. Is that normal for a warm engine on this model?

But if I leave the car sitting for an hour and start, the rpm will fluctuate between 600 and 900rpm... with a slight vibration from the engine through the car
Once I set off and start moving & the engine warms up again it idles back at a standard 700rpm.

Could this just be an issue with one of the cylinders not firing correctly? I ordered a set of spark plugs to be sure as I don't want to end up shelling out £100 for a garage to replace them when I can do it cheaper.

When I took it to a garage the guy said the engine sounded like it was running almost like normal & that the variation could be one spark plug not firing correctly.

[BenS]

Cold start idle is ~1200 and when at temperature 700

The post-1hr-cooldown fluctuation is possibly due to the ECU trying to find the ideal throttle position for the temperature the engine is at.

Regarding spark plugs, they should be changed at the 40k miles service.

[WTF]

Any updates Cube?

[Cubejam]

So the sparks weren't the issue. Was told by another mechanic that it was a firing of one of the cylinders that was causing the inconsistent idle. They were all fine as were the coil packs.

Took it into another garage and they found the it was actually the exhaust. The baffles in the exhaust box had deteriorated & caused a blockage. This caused the pressure to build up and back up back into the engine. Sending all that nasty "soot" back up into the engine contaminating the oil. Required what he called an engine detox to remove all of the oil top to bottom. With that a brand new exhaust box.

Unfortunately not the only story as on top of that he mentioned a whine in the gearbox which he suggests will require a rebuild of the gearbox in time. Can't afford anything like that right now so that will either have to wait (he suggested £800 to £900 and the removal of the gearbox to a specialist). Chances are I will most likely just have to get rid of the car and find something else.

I don't earn enough to be able to afford much of this work and especially not a rebuild of the gearbox. Trading it in for something else is the best option for me I feel :/

Sorry for no replies or updates!