--- Not good news. I had posted a similar whinning noise issue a month ago but had no response. MIne was runnign fine as well apart from the whinning. But I now know what it was. The whining comes from the transmission torque converter (there is pump in there that goes). I had taken it to a mechanic who had said it sounded like timing belt but "bring it back when the CEL or some light starts flashing." Well, no light ever came on, and within another 200 kilometers (canadian) the gears started slipping, mainly number 2. It will seem like you are going over a small hump. Then one morning it would barely move. Towed to a mom & pop transmission shop and here is the whole story:
(1) The torque converter was cooked up. Easy diagnosis for this folks. Showed me one in their shop.
(2) Fix was to overhaul the transmission, no other way because the broken particles from the TC were everywhere in the Transmission.
(3) They had experience with 9 other RX300s - same issue in all. Also the senior (pop) said the same problem on ES300s and Ford Explorers. He had been fixing all these over the years.
(3) He recommended I replace the TC not with the OEM TC but another one which he said is "heavier duty." His has concluded that RX and ES and FOrd Explorers a weak TC in between the engine the the transmission. Cost another a few hundred extra. I went for it because he maintained that those who had taken his advice didn't show up but those wh0 didn't were back within 2-3 years.
(4) He overhauls transmissions himself wiith two juniors. He did mine with an overhaul kit which is made for Toyota, Lexus and GM transmission on some models. Showed me all that comes in there in terms of seals etc. Put in new TC and that was it. Came $1500 below dealer quotes and $1000 below franchise transmission shops. Actually invited me to be present at all times but I couldn't because of work. Had the vehicle out in a day and half.
(5) Drives like new. I have only doen 118k kilometers (about 70k miles)
(6) Has warrantied for 40k kms and said he knows that I will not see him again for another 100k or so. Let's see.
(7) Interesting this fellow maintains there is no difference between Toyota Type 4 oil and the Dextron, He puts in Dextron in all. And it s not the oil changes, but the weaker TC pump, according to him.
So, go to a transmission shop fast while you are still driving and get it checked out.