This paper studies the effect of local thermal nonequilibrium (LTNE) on the thermal instability in a horizontal layer of a Newtonian nanofluid. The nanofluid layer incorporates the effect of Brownian motion along with thermophoresis. A two temperature model has been used for the effect of LTNE among the particle and fluid phases. The boundary condition involved assumes that the nano-concentration flux is zero thereat, including the effect of thermophoresis. The linear stability is based on normal mode technique and for nonlinear analysis, a minimal representation of the truncated Fourier series analysis involving only two terms has been used. The effect of various parameters on Rayleigh number has been presented graphically. A weak nonlinear theory based on the truncated representation of Fourier series method has been used to obtain the thermal Nusselt number, whose variation with respect to various parameters has been depicted graphically.