We investigate the effects of the cooling function in the formation of clumps of protoplanetary disks using two-dimensional smoothed particle hydrodynamic simulations. We use a simple prescription for the cooling rate of the flow, du/dt = −u/τ_cool, where u and τ_cool are the internal energy and cooling timescale, respectively. We assume the ratio of local cooling to dynamical timescale, Ωτ_cool = β, to be a constant and also a function of the local temperature. We found that for the constant β and γ = 5/3, fragmentation occurs only for β  7. However, in the case of β having temperature dependence and γ = 5/3, fragmentation can also occur for largervalues of β. By increasing the temperature dependence of the cooling timescale, the mass accretion rate decreases, the population of clumps/fragments increases, and the clumps/fragments can also form in the smaller radii. Moreover, we found that the clumps can form even in a low mass accretion rate,  10⁻⁷M_⊙ yr⁻¹, in the case of temperature-dependent β. However, clumps form with a larger mass accretion rate, > 10⁻⁷M_⊙ yr⁻¹, in the case of constant β.