the 1st minute or two that you are warming up the car (maybe even 3 or 4 mins on some) have the heater controls on 100% COLD...sounds odd, but otherwise the limited heat that there is will be pushed into the cabin, and so the engine will take longer to warm up. With the heater on cold, all heat is left in the engine bay/radiator etc, and so the engine will warm up quicker.
sorry cant quite see how that works!
the water is there to cool the engine, for the first few minutes the thermostat holds circulation back,until the engine reaches a certain temperature then it opens allowing the cool water to circulate through the heating matrix and engine and thus cool the engine, the by-product of this, is hot water which in turn is used to heat the inside, i think the lexus boys have just wired the heat to start working when the thermostat opens