The influence of simultaneous variation of slip and temperature has been inquired for the case of free-convected flow of an MHD (magnetohydrodynamic), elastoviscous fluid past an unbounded upright plate. How the course of velocity is revamped in response to temperature alterations on boundary has been studied by considering two cases of constant temperature and variable temperature. The inverse and direct role of elastoviscous parameter (K), thermal Grashof number () and Hartmann number (M) in determining the pattern of flow has been discussed through exact expressions and graphical illustrations. Interestingly, a -regime has been identified corresponding to elastoviscous velocity variation. The Newtonian fluid velocity past an unbounded plate entailing slip factor has also been retrieved and compared with elastoviscous fluid velocity. This comparative analysis reflects on magnitude and profile adaptations in response to numerical changes.