That is normal. The heater will never put 100% of the heat to the floor.
There is a TSB to improve the heater operation on the '07 & '08 models. It helps some but not a huge difference.
There is finally a TSB out for the bed bounce issue. It replaces the cab mounts.
T-SB-0270-10 titled CHOPPY RIDE
52216-0C070, 52216-0C020 Stopper, Cab Mount (2)
52217-0C120, 52217-0C160 Bolt, Body Mounting (2)
90177-A0012, 90177-A0012 Nut, Locking…
There was a thread on one of the other forums which says that if you are unhappy with the fix Toyota will replace the whole pedal assembly. Go back to the dealer and complain.
You should understand that the Tundra transfer case does NOT have a differential like a passenger car AWD system. What you are experiencing is wheel hop caused by the different turning radius of the front and rear axles. You should NEVER use 4wd in…