Here is how I start up a Cessna 172-S (IO-360 180HP):

Cold start (oil temp below green arc): Master on, Trottle foward, mixture
foward, fuel pump for 3 sec (look for rise in fuel flow indicator), throttle
to 1/4 inch (about 1000 RPM), Ignition

Warm start (Oil temp in the green arc): Master on, Throttle foward, mixture
foward, fuel pump for 1 sec., mixture back to cut-off, Ignition. When engine
fires, smoothly but quickly retard the throttle to about the 1000 RPM range,
and quickly follow with mixture to full rich.

Hot start (Oil temp in green arc and engine shut down within last 30
minutes): Master on, Throttle foward, mixture foward, mixture back to
cut-off, Ignition. When engine fires, smoothly but quickly retard the
throttle to about the 1000 RPM range, and quickly follow with mixture to
full rich.

I've heard debate on starting the engine with full throttle (make sure you
are firmly on the brakes!). The "Warm start" is a good compromise between
the cold and hot start, and the one I use most often.

Sorry I did not make it clear, we are talking about the Lycoming
IO-360 that is used in the latest Cessna 172's.

The POH is very specific about cold starting: The auxiliary fuel pump
should be turned on and the mixture control pushed in until you see a
rise in the fuel pressure, then the pump is shut off and the mixture
control returned to idle cuttoff.

The POH states that if the engine is hot, the auxiliary fuel pump is
NOT to be used.

Consequently, hot starts are extremely problematic and I can see why:
you are trying to start an engine that was shut down by pulling the
mixture control to idle cuttoff, which starves the engine for fuel,
then trying to restart it with the mixture control in exactly the same
position. Where does the engine get it's fuel to run under those
circumstances? Some people suggest that the POH should be ignored and
the fuel lines primed as per cold starts.

I'm just asking. I'm always ecstatic when I find that the engine is
cold because I know it will start right up using the cold engine start
procedure. Hot starts....

Corky Scott