The smog technician is in control of your vehicle during the smog inspection. Per smog check guidelines they are required to ensure the engine is at operating temperature prior to the smog inspection, only if the vehicle is a 1999 model or older. 2000 & newer vehicles do not need an exhaust sample, thus it does not matter what the engine temperature is.
If your vehicle did need an exhaust sample during the smog check, in other words the smog test was administered on the old BAR-97 smog machine and dynamometer, with exhaust probe, it would have been important for the engine to be at normal operating temperature prior to the smog check.
With that said, if you drove for 15-20 minutes prior to getting to the smog station, sitting for 15-20 minutes with the engine off would not have cooled down the engine enough to fail the smog test unless your car had underlying emissions faults.
Once an engine has warmed up, it would take at least an hour for it to cool down enough to cause a smog check failure... even then, if the smog tech let the engine run for 5 minutes after the 1 hour cool down, the engine would be back at operating temperatures, ready to be administered a smog inspection.
Our general thought on the matter is that if a vehicle fails the smog inspection it more than likely has engine trouble which cause it, rather than manipulation by a smog technician. Undercover BAR investigators bombard smog stations with UC vehicles. It would be unwise for any smog technician to perform a smog inspection without follow the explicit smog check regulations manual.