In this article, the thermal transport characteristics of nanofluid flow through a parallel plate soft nanochannel are researched in presence of the imposed electric field and magnetic field. By incorporating the assumptions of the thermal fully developed flow and the Debye–Hückel linearization, the analytical solutions of the velocity and temperature field for nanofluids are derived. The classical boundary condition of uniform wall heat flux is utilized in the analysis, and the influences of viscous dissipation and Joule heating are taken into account. Furthermore, the Nusselt number indicating intensity of the heat transfer is investigated. The results for relevant dimensionless parameters are presented graphically and discussed in briefly.