The authors take into consideration the placement of the antenna sheet and the transmit/receive modules of the active phased array antenna in its operating position to propose a new efficient design of the air-cooling system for transmit/receive modules with built-in heat pipes of simplified design. This paper presents the results of computer simulation of two alternative designs of the air-cooling system based on a heat sink: a version without heat pipes and one with 16 flat heat pipes with threaded capillary structure. The effect of changing the velocity of cooling air flowing in the heat pipe channels from 2 to 10 m/s on the temperature field distribution and the temperature of the hottest transistors is demonstrated for both versions at a total thermal power of 8 transistors amounting to 224 W. At an air velocity of 2 m/s, the use of heat pipes in the cooling system made it possible to reduce the temperature of the hottest transistor by 20 K, and at an air velocity of 10 m/s, by 14.9 K. The recommended air velocity in the heat sink channels was determined to be in the range from 4 to 8 m/s, in which the temperature of the transistors is reduced to 33.3% compared to the heat sink design without heat pipes.