A computational study for investigating the flow and heat transfer phenomena in the unsteady magnetohydrodynamic couple stress dusty fluid flow over a linearly stretching porous surface in the presence of viscous dissipation effects is presented. The governing equations, in nondimensional form, are tackled by the exploitation of the standard spectral quasi‐linearization methodology. The estimations of flow rate and temperature profiles are pictured diagrammatically. In contrast, the local skin friction and heat transfer rates are placed in tabular form for various values of thermofluidic parameters. The numerical results of a current investigation are compared with previously available results and located to be sensible agreement as shown in Tables 1 and 2. It is analyzed that by elevating the specific heat parameter and couple stress parameter, the temperature profile and the resulting thickness of the boundary layer are depressed. In comparison, an increase in thermal boundary layer thickness and a decrease in thickness of the momentum boundary layer were found with the rising magnetic parameter values.