Whining Noise When First Started

Anyone ever run into having a whining noise when you first start up the motor? I have an '05 TB and whenever it sits for at least 45 mins to an hour when I go and start it, it will make this whining noise like some kind of electric motor is running. It goes for about 20 seconds and then it stops. And it only does it after it sits for a little while if you stop it and then start it right aways it wont do it again.

Before you do anything else, pay close attention to some cold starts, like in the a.m., for whether you can hear it then, too. Absent the SES idiot light coming on, my hunch is it's the fan clutch doing its job (spinning the fan). The 20 secs or so would be normal start-uo engagement time, then it releases until/unless your engine temp kicks up enough (say, hot day, stop & go traffic, A/C on) to require it to re-engage. The sounds you hear from under the hood can be influenced by where you're parked, so take those accoustics into account also.