This paper deals with the nonlinear stability dynamics of nanofluid convection under magnetic and temperature variation for Copper Oxide (CuO) nanofluid, which is used as coolant in heat transfer applications. The system comprises a cavity in which the fluid layer is subjected to external magnetic field and heat exposure. The partial differential equations of conservation of momentum and energy are the governing equations, which are converted to a system of nonlinear differential equations. Using stability, phase portrait and time series analysis, the effect of magnetic field and temperature variation through Hartmann number and Rayleigh number on the chaotic CuO nanofluid convection is studied. It is observed that as the value of Hartman number increases, then the system enters into a stable phase. However, on increasing the Rayleigh number system becomes chaotic. Also, it is observed that by controlling the Rayleigh number chaos cannot be controlled but only on increasing the applied field the chaotic state in nanofluid convection can be controlled, which indicates towards a kind of magnetic cooling. It is concluded that as temperature varies the nanofluid convection exhibit chaotic motion which can be stabilized by applying magnetic field which has many applications in drug delivery, nano technology, environmental engineering, industrial engineering and in pharmaceutical industry.