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In the field of heat manipulation, active thermal cloaks based on thermoelectric chips (TECs) have received much less attention than passive thermal cloaks based on metamaterials. This work focuses on active thermal cloaks and explores in-depth their mechanism of heat flow regulation. For a two-dimensional circular object located in a rectangular background plate with uniform temperature gradient, the theoretical design of an active cloak was realized by analytically solving for the target temperature field. A parameter study was conducted numerically for the designed thermal cloak. The results show that the object-to-background thermal conductivity ratio (m) is the key parameter that determines the working mode of the cloak. When m < 1, the TECs work in a heating mode with less power consumption; when m > 1, the TECs work in a chilling/heat pump mode with higher power consumption. If the change of a certain parameter increases the heat flow regulation, it will also cause performance degradation and an increase of the thermal cloak’s power consumption, especially when m is greater than 1. Improvement can be achieved by increasing the number of TECs (N), but the impact of N diminishes rapidly beyond a certain value. The systematic study in this work reveals the high flexibility and wide adaptability of the TE-chip-based thermal cloak in heat flow regulation.