Thanks for your response.
Well, the little darlin's been asleep for a while, so I woke it up. No fan for about 10 minutes this time; I opened Safari and went to Yahoo, then opened Illustrator, nothing taxing, but still no fan. Then I connected an external disk and opened some windows, preparing to install some System updates. Now the fan came on.
It sounds like just the one in the right rear, I.e. the power supply fan -- perhaps because of the power draw from the external HD? I disconnected the power adapter, but the fan still continues ten minutes later. And earlier when I wrote the above, from how loud it was I'm guessing both fans were going, though there was no external HD connected at first, and all I'd done was start it up and run Software Update.
I disconnected the external HD; with the power adapter still disconnected (running on battery), the fan is still going: air coming out the vent on the right side, but not in the back or on the left.
Now the fan has stopped. Activity Monitor shows itself using 3.5% CPU, SystemUIServer using 0.5%, everything else at 0.
Connect the external bus-powered FireWire HD again, and the fan comes on again in a minute or two. After ten minutes or so I disconnect the external HD, then the power adapter; fan still on, stops after five minutes. Which reveals that the CPU (center) fan is running, though the computer's doing nothing other than displaying the Finder.
Ambient temperature's about 80F; humidity is 3% here in the high desert. The PB is sitting on a table on its rubber feet, so it has some air flow. The bottom is warm, but I wouldn't call it hot; I can rest it on my hand with no discomfort.
I have a 12" PowerBook (1.5GHz); I've noticed its fan comes on a lot (more than my MacBook Pro 17" 2.5GHz, which commonly has maybe a dozen apps open but seldom makes fan noise - though I know its fancy variable fans can be quiet), but it does have to be doing some actual work first.
This TiBook crams twice the speed into the case originally designed for the first 400/500MHz model, so I guess it shouldn't be surprising if it runs a little hot. It seems excessive though for the fan to be running all the time even when the computer is idling. Constant fan noise drives me nuts, like a ringing phone it feels like a demand that I DO SOMETHING. I'll be asking the owner of this TiBook tomorrow if she's used to it doing this.