Toyota - Yaris :: 2009 - High Pitched Whining Noise Getting Louder With Accelerator

I have a 2009 Toyota Yaris with 35,000 miles, and fully up-to-date with all the 5,000-mile usual maintenance checks [no prior problems]. Driving on a hot day, I hit Bakersfield and the car started to make a high-pitched whining noise, which got louder with the accelerator and softer when I took my foot off the gas. I thought perhaps the car was overheating and let it rest for a while, and checked the coolant [which was at a normal level]. I finished the drive to LA and stopped by the Toyota dealer who said it must have just been the fan given the hot weather.

The noise went away overnight, but the next day I was driving around town when it was overcast and cool, and even driving locally, the car made the whining noise intermittently, especially loud at low speeds like coasting in a parking lot, and the noise has been getting louder and sounding more pathological--not like a normal engine or fan noise, but like a truly problematic high-pitched straining sound. Sometimes it comes on when I start the car, sometimes restarting the car makes the noise go away for an hour or two.

It sounds almost like an electric razor being whipped around like a numchuck - a hitch pitched whine that is rotating in the engine and speeds up with the accelerator and calms down but doesn't go away at a stoplight. Perhaps I finally ran over my neighbor's annoying kitty. But today's latest Toyota mechanic also couldn't figure it out because the noise didn't start when he turned on the car and didn't restart on his test drive, but only a few hours later after I'd driven the car around town.