Abstract Mathematical simulation of unsteady natural convection in an inclined cylinder with heat-conducting walls of finite thickness and a local heat source in conditions of convective heat exchange with an environment has been carried out. Numerical analysis has been based on solution of the convection equations in the dimensionless variables vector potential components, modified vorticity functions, temperature. Particular efforts have been focused on the effects of four types of influential factors such as the Rayleigh number Ra = 104, 5 · 104, 105, the Prandtl number Pr = 0.7, 7.0, the thermal conductivity ratio k 2 , 1 = 5.7 · 10 - 4 , 4.3 · 10 - 2 and the inclination angle γ = 0, π/6, π/3, π/2 on the velocity and temperature fields. The effect scales of the key parameters on the average Nusselt number have been determined.