Replaced both fans
Much fan noise. Sometimes the machine ran normally. At other times one of the fans would actually seize up briefly, then restart. I think it was just the right fan (which is actually to the left when you flip the computer over to remove the bottom of the case). I replaced both fans to be on the safe side.
Earlier I had tried simply cleaning the original fans. Opening the computer and removing those fans (following iFixit's instructions) revealed they weren't all that dirty. There was a bit of lint, but not enough to seriously impede airflow. I blew the lint out with compressed air. But after replacing the fans, the noise, if anything, was worse than before. And so I ordered replacements and installed them.
Fine. The badness is gone.
The only confusing part is detaching the four-wire connectors from their sockets. iFixit's instructions are correct that they lift straight up. The advice not to break the socket off the logic board is gratuitous. In fact, the connectors lift off and reconnect easily.
MacBook Pro 15" (Late 2008-Mid 2012 excluding Mid 2009 2.53 GHz) Left Fan
MacBook Pro 15" (Late 2008-Mid 2012 excluding Mid 2009 2.53 GHz) Right Fan