The focus of the article is the electro-magneto-hydrodynamics of an Oldroyd 6-constants fluid flow through parallel micro-plates with heat transfer. The medium between the micro-plates is porous and we use the Darcy-Brinkman-Forchheimer model for it. Numerical calculations, using the shooting method, were performed to solve the non-linear equations that emanate from the modeling. The results for the velocity mechanism, the Nusselt number and the temperature distribution are graphically shown. The analysis of the problem focuses on the effects of several fluid and heat transfer parameters, such as the Hartmann number, the Brinkmann number, the Darcy-Brinkman-Forchheimer parameter, the Darcy parameter, the viscous dissipation, and the Joule heating coefficient.