Electrokinetic flows through narrow confinements have mostly been studied with symmetric boundary conditions on the walls even though in practice it is very common to have these walls made of different materials which in turn lead to different surface charge conditions on them. Such a dearth of studies is particularly acute in streaming potential flows which are naturally predisposed to strongly influence even simple pressure-driven flows in such narrow confinements. Further, the very nature of the fluid may, in general cases, be of non-Newtonian nature; this is especially true for biomedical assays. Motivated by this, we address a model problem of a streaming potential mediated flow of a power-law fluid through a slit channel having different boundary conditions. Additionally, as an important new contribution to this line of investigation, we study the thermal characteristics of such flow. Noting, pertinently, that the streaming potential effects are especially stronger for high values of the surface charge (which translates into high magnitudes of the zeta potential), we present a general framework that incorporates steric effects of the ions. This is done to avoid the unphysical ionic distributions predicted by the traditional Boltzmann approximation.