We study a shot noise of a wide channel gated high-frequency transistor at temperature of 4.2K near pinch-off. In this regime, a transition from the metallic to the insulating state is expected to occur, accompanied by the increase of the partition noise. The dependence of the noise spectral density on current is found to be slightly nonlinear. At low currents, the differential Fano factor is enhanced compared to the universal value 1/3 for metallic diffusive conductors. We explain this result by the effect of thermal fluctuations in a nonlinear regime near pinch-off, without calling for the enhanced partition noise.