I've noticed this of late. An irritating rattle from the driver's side door, but the key is that it only happens when the temps are cool. If the car is warm/hot due to being out in the sun, there is no rattle. This tells me it's something resolved when heat makes parts expand, but if I can stick something in that will stop the rattle altogether, I'd prefer to fix it. Any clue what's causing it? FWIW, pressing on the door in various places hasn't helped to stop it, so I doubt it's the door panel itself. Likely something inside it or behind it.
I have come to the conclusion that in any car you buy nowadays there is going to be a rattle or a squeak that we are going to have to find some way to live with and I probably hate them worse than anyone on the planet. These things just seem to come out of nowhere.
Are you sure it is the door? I had a rattle that sounded like it was coming from the door, when actually it was the seat belt clip rattling up against the door instead.
Have you tried driving with the driver's window rolled down - does it still rattle? If not, then it's in the inner mechanism beyond the door panel. You might have to remove the door panel to further diagnose the noise.
Lowering the window is no help...that I can tell. I can't hear it over the wind noise. It's not that loud, but I have sensitive hearing and am a HFA...so it really annoys my senses because it's right in my ear. The center console was obnoxious, but I did the "fix" for that and largely eliminated it. I was hoping it would be something simple with body panels I could just stuff a bit of foam into a crack to stop the rattle.
Removing the door panel and subsequent tarred cellophane to get access inside the door cavity is a major undertaking. I've been inside mine to add the Dynamat, but this sounds like a task for the dealership. Too bad you did not discover it just after purchasing it (I assume you are the original owner) as they would have probably taken it apart under warranty. It's even possible someone put a "part" in the door cavity as a joke during the manufacture as one member here found a ball bearing in an area under the seat. Others have reported rattles of foreign objects in the headliners too.
Latest development. I tried pressing and pulling in several places. For some reason I tried poking places with the toe of my shoe while driving. I hit a spot that turns out to be a support brace for the fuse block. When I pulled gently back on that, the noise stopped. I noticed the noise was coming more from the steering column than the door, so I don't know if I was hearing an echo or if it's a different noise altogether. Getting home, I can find nothing obvious causing the rattle. I tapped about but couldn't reproduce it or see anything obviously loose causing the problem. It could be as simple as a wire harness tapping against another part.
I have a new 2014 Avalon Hybrid. I am having the same problem as you are having. I have a SOMETIMES RATTLE. I just can not figure out where it is coming from. I despise rattles but I am almost convinced that I will never find this one. If you had someone (which I do not have) that could ride with you in the car and listen and look for the rattle while you drive might be an idea. I have never used one but I would be willing to buy a stethoscope to listen and look for it. Sears has a stethoscope for mechanics that is called LISLE STETHOSCOPE that is for sale online for less than$20.00 that is used by mechanics. I would try it. I would try anything but unfortunately I have no one to ride with me.