Our proposal, a topology optimization method for thermal carpet cloaks, eliminates the disturbance caused by a bump obstacle on a flat boundary and, despite the presence of the bump, reproduces the temperature distribution as if no bump is present. Structural topologies are expressed using an immersed-boundary level-set method and the optimal topologies corresponding to the optimal sets of the level-set functions are explored using the covariance matrix evolution strategy for minimizing the difference between the temperature field under a flat boundary and that for a cloaked bump on the boundary. The difference is evaluated as an objective function and, in the best instance, this function value for the optimal cloak approaches a value 0.000214% of that when no carpet cloak is present around the bump. By moving the location of the heat source, we investigated the performance response of the topology-optimized thermal carpet cloaks for different angles of heat flow. The thermal carpet cloaks presented exhibit good cloaking performance for heat flowing over a wide angle. (C) 2019 Elsevier Ltd. All rights reserved.