This paper is the second part of the article on the same title (the first one is devoted to flow resistance). It presents the results of numerical studies of heat transfer in a circular tube with a turbulising ball insert and is focused on an analysis of the influence of its geometry (i.e., ball diameters and longitudinal distance) on the heat transfer intensification in the turbulent flow. The investigations were conducted for a range of Re = 10,000 divided by 300,000, different diameters of the balls (Db = 7, 10, 13, 16 and 19 mm) and various longitudinal distances between them (L = 20, 24, 28, 32, 36, 40, 48, 60 and 85 mm). It was observed that for the tested range of ball diameters and their longitudinal distance, there was an analytical formula that allowed one to express the Nu number by a relationship in the form Nu = C center dot Re-D center dot Pr-0.4, where the constants C and D were defined as a function of two variables: the ball dimensionless diameter (X = Db/Dp) and the dimensionless longitudinal distance (Y = L/Dp). These constants are closely related to each other and can be calculated analytically for the entire range of X and Y using a formula of the fourth order surface polynomial (15 coefficients of this polynomial for both C and D constants are presented in this paper). For the tested geometries, an increase in the intensity of heat exchange by a few times was obtained depending on the ball spacing and diameter (with respect to the tube without an insert). The thermal characteristics Nu(Re) of inserts for all these parameters and geometric configurations are presented on diagrams. (C) 2014 Elsevier Ltd. All rights reserved.