This paper presents the motion of unsteady gravity-induced nanofluid flow containing gyrotactic micro-organisms along downward vertical convectively heated surface subject to passively controlled nanofluid. Considering the influence of temperature on the dynamic viscosity during convection and nature of thermal conductivity during heat conduction processes, these thermophysical properties are treated as linear functions of temperature. The governing equations are nondimensionalized by using suitable similarity transformation. The dimensionless nonlinear coupled PDEs are solved using a new pseudo-spectral technique called paired quasi-linearization method (PQLM). Convergence tests and residual error analysis are also presented to validate the accuracy, solution error, and computational convergence. The proposed PQLM yields accurate results which are obtained after a very few iterations. Minimum coefficients of with Sc are obtained at final steady stage.