Characteristics of two-dimensional heat island convection under general flows are investigated by numerical and laboratory experiments and the results are compared with those of the linear theory in Part 1 (Kimura, 1976). The aim in Part 2 is to examine the effects of 1) self-advection due to the convective motion, 2) vertical shear of the general flow, 3) Prandtl number and 4) ground temperature distribution upon the heat island convection. The main results obtained in the present study are as follows: 1) The self-advection has an effect to concentrate the updraft in a small area at the center of the heat island as stated in Kimura (1975), but the effect is reduced with the increase of the general flow. 2) The vertical shear of the general flow has an effect to increase the height of the inflow region of the perturbation flow field. 3) The small Prandtl number favours the development of the upstream perturbation in the middle layer as speculated in Part 1. 4) In Part 1 maximum values of the perturbation horizontal velocity (umax) decreased monotonously with the increase of the general flow, but in Part 2 it was found that umax is constant or slightly increases under the weak general flow for the more general ground temperature distributions than the form assumed in Part 1. 5) These effects shown in 1)~4), however, are not so significant as to alter the main features of the heat island convection obtained in Part 1.