Theoretical considerations on convective heat transfer from isothermal upward conical surfaces have been presented. The physical model of this phenomenon consists of an isothermal cone of inclination angle (phi) between the cone generating line (X) and the radius (R) of the cone base. The angle is a parameter of conical surface which varied from (phi = 0-circular horizontal plate) to (phi = pi/2-vertical cylinder). On the basis of Navier-Stokes equations, assuming the parabolic temperature profile in the boundary layer, the velocity profile tangent to the surface has been calculated. Introduction of the mean Velocity value in the boundary layer into the balance of energy and mass equations and comparison with the Newton equation leads to the dependence describing the boundary layer thickness. Next the relation of Nusselt and Rayleigh numbers, including a function expressing the influence of the inclination angle (phi) on the heat transfer process, has been derived. The obtained solution describes the natural convective heat transfer process for three characteristic cases of the conical surface. For the boundary cases phi = pi/2 (vertical cylinder) and phi = 0 (circular upward facing horizontal plate), the solution describing convective heat transfer intensity is Nu(X=H) = 0.668.Ra-X=H(1/4) for phi = pi/2 and Nu(X=R) = 0.932.Ra-X=R(1/5) for phi = 0. For the case (0 < phi < pi/2) (cones), the solution has the form Nu(X) = 1.680.Phi(1/4).Ra-X(1/4) where (Phi) is a function of the inclination angle (phi) of the generating line of the conical surface to the base of radius (R).