2000 RAV4 engine ticking noise: ideas?

[kavatski]

Recently bought a 2000 RAV4 4WD auto, has about 48k miles on it now but only about 600 of those are mine. Ever since I got it I've noticed that when it's running there's a ticking/clicking noise coming from something on the driver's side of the engine bay about halfway back. Doesn't seem to be coming from the engine block itself.

The part I can't figure out is that the noise only shows up after I've driven a few miles and the engine's warmed up. BUT, if I turn off the engine while it's ticking, then IMMEDIATELY re-start, it doesn't tick. Only after I've driven another mile or two does it start ticking again.

Can't hear it while driving but at idle it's noticeable from inside the car. It's not the A/C or the exhaust.

Anyone have an idea what could be making this kind of a noise? Described it to the dealer's service rep over the phone and he had no idea. I've had valves or injectors suggested to me as the culprit but I'd expect to hear those making a noise all the time. Why can I make it go away for a couple of miles by re-starting the engine?