AbstractWe consider an unsteady non-isothermal flow problem for a general class of non-Newtonian fluids. More precisely the stress tensor follows a power law of parameterp, namely$\sigma = 2 \mu ( \theta , \upsilon , \| D(\upsilon ) \|) \|D( \upsilon ) \|^{p-2} D(\upsilon ) - \pi \mathrm{Id}$σ=2μ(θ,υ,∥D(υ)∥)∥D(υ)∥p−2D(υ)−πIdwhereθis the temperature,πis the pressure,υis the velocity, and$D(\upsilon )$D(υ)is the strain rate tensor of the fluid. The problem is then described by a non-stationaryp-Laplacian Stokes system coupled to an$L^{1}$L1-parabolic equation describing thermal effects in the fluid. We also assume that the velocity field satisfies non-standard threshold slip-adhesion boundary conditions reminiscent of Tresca’s friction law for solids. First, we consider an approximate problem$(P_{\delta })$(Pδ), where the$L^{1}$L1coupling term in the heat equation is replaced by a bounded one depending on a small parameter$0 < \delta \ll 1$0<δ≪1, and we establish the existence of a solution to$(P_{\delta })$(Pδ)by using a fixed point technique. Then we prove the convergence of the approximate solutions to a solution to our original fluid flow/heat transfer problem asδtends to zero.