In spintronic-based neuromorphic computing systems (NCSs), the switching of magnetic moment in a magnetic tunnel junction (MTJ) is used to mimic biological neuron firing. However, the high currents required for MTJ switching will lead to a large energy consumption and low speed operation of the MTJ-based NCSs. In this paper, the energy consumption and the delay of the proposed MTJ-based NCS are reduced by thermally assisting the MTJ switching through a microwatt nanosecond laser pulse. Simulation results show 85.7%, 84% and 97.8% improvements in energy consumption, delay and energy-delay product, respectively, for the laser-assisted spintronic NCS (LAS-NCS) by heating the MTJs up to 127°C. The energy consumption of the laser pulse for heating up the MTJ stack is 1.2X-2.4X lower than Joule heating method. Moreover, in contrast with Joule heating method, the LAS-NCS does not require MTJ with modified structure.