Start with the easy stuff.
Test the A/C compressor as Doubelieve suggested.
If you don't know what it is or where to look, might try driving and flip the A/C on or off when the noise happens so you can rule that out.
Little noises are the kind of thing shops don't really want to waste their time on, they usually aren't able to charge much for the time spent.
I say get the chassis ear and hunt down that noise! You don't need to know what anything is, just don't put anything close to spinning parts. I've never used one, but always wanted to try it.. so you should get one and write a review