"It has nothing to do with coolant temp." Needs a little more explanation
On each start up, all engine sensor data, (including coolant temp data) is stored in a file in the PCM. The data is stored until the drive trip is terminated, then the PCM dumps the file. There are several "cells" programmed into the PCM. Each cell contains a set of parameters to use under different operating conditions for injector pulse width, ignition timing, etc etc. The expected time frame for the HO2S to reach its operating temp is included in whichever cell is in use. The PCM does not monitor coolant temp during warm up for the purpose of timing the HO2S. That data is already in the cell and determined the instant the ignition is turned to the ON position, before the starter even engages. If the HO2S exceeds that time before it starts switching, the DTC is set.