I have no need so I haven't mixed in the discussion. Any timer would likely work, the discussion seems to be the best way to wire it. Which in my opinion is kind of overkill, it isn't that complicated.
I'd likely mount a Kixon (primitive thermostat) onto the fuel rail and have the aux fan come on if a certain temperature is achieved. Not that big of a deal, wire in another relay (maybe a diode).
You can likely check to see if heat is your problem, by cracking the hood the next time you shut down on a hot motor and see what happens after ten minutes. If the problem disappears it is likely the heat.
On Renix models the CPS was somewhat heat sensitive, the resistance values changed with the heat. A marginal CPS would malfunction with temperature changes. I surly don't know if this is an issue in the later models or not.