Currently driving a thail built honda fit/jazz with the 7 speed tiptronic CVT. car is completely stock except for a spoon catback muffler (b pipe and axle back) and using 16" Buddy Club P1 Challenge rims on Toyo Proxie 4 tyres. ( note: stock intake)
Honestly I have to say with lower profile and wider tyres the car is heaps better, handling wise. theres more stability and greater cornering speed compared to the stock 14" yokohama aspec tyres that came with the car.
didn't really have problems with brake fade while on the track (Winton Raceway, Benella Victoria Australia) however it was noticeable the next day while driving the car. Seems to have a very spongy feel the next day.
would recommend any jazz/fit owner to take theirs to the track auto/manual.