AbstractThe aim of this article is to investigate the steady two‐dimensional flow of a magnetohydrodynamics Maxwell liquid over a stretched exterior having prescribed exterior hotness in the presence of changeable free stream temperature. Here the Maxwell liquid replica reflects non‐Newtonian liquid behavior. By means of similarity alterations, the leading differential equations which are partial in nature are altered to differential equations that are ordinary in nature and subsequently numerical solutions are received via a shooting scheme. The motion and heat transport characteristics for the leading parameters is scrutinized and talked about elaborately using their graphical demonstration. It is established that the liquid speed reduces with escalating magnetic parameter. The consequences of growing Maxwell parameter are to hold back the speed of liquid. An increment in heat movement speed has been observed for enhancing the temperature ratio and Maxwell parameters.