Ive just read your last post properly and it seams its fine now?
If the car is over heating sitting for 2-3min is not going to do anything. The water temp actually goes up when you turn the car off due to heat soak
 
I would not expect changing to a genuine thermostat will make make any difference except for reliability. 

It's been the same scenario 3 times now. I drain/refill system, I drive, it overheats. I wait 5-10 mins (heatsoak?) it stabilises. Maybe the thermostat opening point is higher than 80 C. Water pump is worst case mech says. I don't really have anymore corners to look at besides the genuine thermostat, which I have already placed an order. Ironically, my Toyota dealer keeps thermostats in stock but not the gasket...
 

The last time I got a new genuine Toyota thermostat it had the perimeter gasket included in the box.
Maybe you have to buy a thermostat to get the gasket, lol.
 

Update. Got the genuine thermostat today and it wasn't too bad doing it myself. Although specialised tools really helped, especially the knuckle type connector for the ratchet - biggest life saver and mirrors.
dasic1 I hope you were gonna be wrong but unfortunately for me you were right grrr lol
This time when I was refilling the car, the radiator bleed valve didn't even purge any air at all!! Definitely something in the system blocked or plumbing fugged.
Time to see the specialist doctor...

another victim of the most complicated cooling system in the world... LOL :P
radiator blocked up maybe?

He's recently fitted a new one.

Ah ok...do the thermo fans operate?? all i can think of after that is the water pump is non genuine and shagged.

Man I had no probs with it before the engine swap everything was going fine until I blew the old motor lol. Radiator is brand spankin new (given how long I've actually driven the car)
Oh yeh here's the difference between genuine and non genuine:
 

Notice the extra bit in the centre on the genuine one? Still doesn't solve my problem tho grrrrr

are you sure the coolant isnt going into the engine???
dont mean to scare you but your pouring heaps into it but its not reaching the radiator so it must go somewhere??
ist either that or not circulating and boiling  in the block which is why yuo are getting overheating..
 
i would redarin every last drop of coolant fill it with water and make sure you have put in 13 litres atleast, then see what happens

also are you leaving the heater on full hot setting so that water gets in heater core as well