Engine temp is used as a base line to set mixutre (that and MAP
sensor at startup determining pressure altitude) so it is conceivable
that it could effect idle but it would likely have running problems
too.
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TheSnoMan.com

What model and year is the vehicle?

JAM

Yes it can....but...

When a coolant temp sensor give an incorrect reading it causes the fuel mix
to be either too rich or too lean. If your oxygen sensors are working
correctly they will sence the rich/lean mix and the pcm will compensate for
it. You would probably not notice this when driving the vehical. What you
would notice is the idle speed may be too high or too low as this is the
sensor the pcm looks at to set idle speed. Depending on how new your vehical
is the pcm could still give a fairly correct idle speed by looking at other
sensors and/or calculating run time.

It looks like it's time to get a scanner on it instead of throwing parts at
it. It may save you some money in the long run.

Denny

It is very posible.  IIRC you disconnect the temperature sensor to check the
timing.

beekeep