When pit foot on gas the revs seem to have no power then suddenly lurches forward

The gearbox oil and filter or screen

Torqu converter clutch seems bad, drive uphill with 1 foot on gas & tap brakes at same time, if engine revs up, this is the problem

ignition modules can cause problems like this also airflow meters and faulty fuel pumps

Sounds like the torque converter isn't unlocking quick enough. Drive at 45mph,keep foot on gas and use other foot to touch the brake and watch the tach to see if it speeds up,when converter releases. Check trans fluid level hot.If it is more than a couple years old,change. Use the correct fluid for Toyota and add a bottle of Lubgard. Have the throttle positon senor scanned and check any idle control circuits. Throttle Body may need cleaning.

This sounds like a transmission problem. I am haveing a simular problem. Shifts to drive, but is slow to catch and if you apply gas before engage it lurches forward. I am having the transmission replaced with a used one with less miles.

sounds like one of the metal arms connected to the engine may be getting stuck some how. have someone get in car and press on gas when car is off while you watch engine to see what is moving, then check those arms to see if there is any possible obstructions or knicks or something on them

I would have to say that your transmission failed. The Tranmission was trying to lock up and the engine was being forced to labor extra hard and that is what more than likely created the extra heat.

It sounds like you may have lost your water pump or your thermostate may have gone bad too. Regardless if your going to change your water pump your going to have to change the thermosate too. 
As for the transmission it could be your spider gears , there weak in the 700R4 and other you lose your reverse first with had lurchs when put in to drive. Sorry for the bad news, good luck

try going to a muffler shop and have the catalytic converters checked i am sure that is your problem when they clogg up it wont keep speed and then take off

disconnect the egr valve and try it at low speed if you give some gas egr open to mush to mush air not enought gas create hesitation before changing the egr just disconnect it and try hope it FIXYA our problem thanks pierre