We consider the flow and heat transfer in an elastico-viscous fluid between two co-axial infinite porous rotating discs for small cross-flow Reynolds number. The discs are rotating with different angular velocities, and the rate of injection of the fluid at one disc is different from the rate of suction at the other disc. The governing equations are solved by perturbation method, taking cross-flow Reynolds number as perturbation parameter. The analytical expressions for radial, transverse, and axial velocity components and temperature are obtained, and these results are numerically analyzed for different values of parameters involved in the solution.