This work studies the natural convection heat transfer about a vertical cone embedded in a tridisperse porous medium with constant wall temperature. The three-velocity three-temperature formulation is used to derive the governing partial differential equations. The coordinate transformation and the order-of-magnitude analysis are then used to obtain the nonsimilar boundary layer partial differential equations. The cubic spline collocation method is then used to solve the nonsimilar boundary layer partial differential equations. The effects of two inter-phase heat transfer parameters, three modified thermal conductivity ratios, and two permeability ratios on the heat transfer and flow characteristics of the tridisperse porous medium are studied. Results show that increasing the three modified thermal conductivity ratios or the two permeability ratios tends to increase the natural convection heat transfer rate of the vertical cone in a tridisperse porous medium. Moreover, the thermal non-equilibrium phenomena between the three phases of the tridisperse porous medium are affected by the streamwise coordinate and the two inter-phase heat transfer parameters. The thermal non-equilibrium effects between the three phases of the tridisperse porous medium become significant as the two inter-phase heat transfer parameters or the streamwise coordinates are small.