I was hoping (but not expecting) that Epson might indicate what factors and sensors were being used to set the fan duration on startup, as I was curious - but I wasn't surprised with their less than detailed answer. My projector starts up in virtually identical conditions each time - it's usually been sitting for days, ceiling mounted in a cool basement room that is probably almost always right about 18C/65F in temp. As stated, the fan runs for variable durations when it starts. Their startup logic could be looking at any number of things other than temperature, such as number of starts, total run time, time since last start, duration of last power up interval, average run time, etc. It could be a combination of stored variable data points and real time sensors like temperature, voltage, rotational speed of the fan, power draw, etc. They could be using the occasional extended fan interval to help purge dust, or to ensure the bearings remain noise free over the life of the projector. Who knows? (Beside Epson)
Bottom line for me - I don't really care, as long as it works.
If my projector consistently failed to light on startup, with the orange 'lamp error' indicator, I would be more concerned about that. I believe that happened once shortly after receiving the projector, and I simply cycled the power and was back in business. If it was a regular occurrence I'd be contacting Epson support about it. That sounds like a likely candidate for a firmware fix, as there does not appear to be any actual fault based on the reports I've seen so far. If a simple power cycle fixes it, they should be able to make the system verify the 'bad' reading in the initial startup by clearing any internal registers and checking it again, doing a second start attempt on the bulb, etc.
As mentioned, it could be a bad bulb issue - perhaps some bulbs have a higher internal resistance to starting than others, and a simple swap would eliminate the problem. If you do go that route, please let us know the results.