Transformation thermodynamics has potential applications in heat flux management. The geometrical transformation used in the cloaking procedure requires materials that are inhomogeneous and thermally anisotropic. This requirement can be reduced by segmented cloaking, where materials with homogeneous and isotropic thermal properties are adopted. One of the issues when constructing a segmented cloak is reducing the number of segments and yet preserving the performance of the thermal cloak. In this study, the performances of linear and nonlinear segmented cylindrical cloaks are assessed, by comparison with the performance of a single-layer thermal cloak based on inhomogeneous and thermally anisotropic materials. The possibility of finding an optimal balance between the number of segments and the efficiency of the segmented cloak was investigated. The study shows that introducing a thin insulating layer inside the segmented cylindrical cloak improves its performance.