coolant temperature sensors are critical and fairly cheap ..
also if you want to check your engines condition,
try a compression test,
if its ok,
check the exhaust system for leaks (they generally leak from ex.manifold gaskets)
and also check for air leaks by spraying carb cleaner around engine...
must add, rough idles can be caused from many components which I spent a fortune on it in the past 
and also hot and cold idle problems differ..
Engine ok, 4 year old GM transplant with 60K miles on it.
No exhaust leaks.
Practicaly cleaned the engine with high flameable gasses and liquids.
And, it's a hot idle problem 
is it surging up and down ?
does the engine shake randomly ?
ps: 4 yr old and 60k doesnt guarantee anything imo :-/
It shake randomly, then it will be okay for some seconds, and then shake again. The engine whas tested for vacum leaks with some carburettor cleaner and "starting gas" ?? on the outside only, without any luck.
When this heppens, the live data from the O2 sensors go from lean to rich, but does not create a fault code.
I have changed the crank sensor after a intermittent 31 code, and the starting problem dissapeard, like the 31.
The engine is checked, and the timingbelt and compression is ok, so is the color of the spark plugs, they all look the same.
There is no back compression in the system, and the crankhouseventilation works fine.
Cant find enything wrong with the live data from my diagnostic either, but I'm going to test my sons 2,5V6 with the diagnostics to compare, just have to wait until he comes back from school for a weekend

So I'm still confused, because the car runs good, and slightly pulls ahead other 2,5V6's.
So, my question is:


?? :-/