The most logical suspect would be a noisy wheel bearing, but those typically make noise all the time relative to wheel speed. Temperature isn't generally a factor either.
There is a tool you might be able to borrow or rent from an auto parts store that borrows them called the "Chassis Ear". It is a set of six microphones, a switch box, and headphones. You clip the microphones to suspect points, then drive around while listening with the headphones. You can move the microphones around to zero in on the source of the noise. Be aware that many mechanics have never seen or even heard of this tool. Suspension and alignment mechanics use it to find rattles, squeaks, and other noises.
The guys who drive the tool trucks around to shops during the week can get them too, but they are also available on the Amazon web site for about one third the cost.
An air leak is another suspect. The engine is going to rock when under load, and that will tug on vacuum hoses and fresh air tubes. Along with just raising engine speed in your garage, do that while it's in gear and you're holding the brakes on.
The Chassis Ear is real effective with noises that are being transmitted through metal parts or other hard surfaces. It's not as effective when the microphone is in the proximity of a noise near something soft, like rubber hoses or plastic air ducts. You'll still hear those noises but the source is much more obvious when it's coming from metal parts.
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Saturday, January 11th, 2014 AT 3:35 PM