In a fast incore thermionic spacecraft reactor for nuclear propulsion, the temperature rise due to the neutron heating in the reflector control drums is investigated. The reactor is fuelled with (U-Ta)C, consisting of 80UC-20TaC with a sinter density of 80 and controlled with the help of rotating drums imbedded into the beryllium reflector. The control drums contain natural B_4C strips (with 20 ~10B and 80 ~11B) and produce nuclear heat via neutron absorption in ~10B. The neutronic analysis has been conducted in S_16 -P_3 and S_8 -P_3 approximation with the help of one- and two-dimensional neutron transport codes ANISN and DORT, respectively. Calculations are conducted for a reactor with a core radius of 22 cm and core height of 35 cm leading to ～ 50 kW_el in power phase. Reflector drums with 100 natural B_4C in form of strips (drum diameter = 13.5 cm, strip width = 5 mm) at the outer periphery of the radial reflector of 16 cm thickness would make possible reactivity changes of Δk_eff,max = 10.7 without a significant distortion of the fission power profile during all phases of the space mission. A reduction of the B_4C in the strips to 20 and 10 would still allow a reactivity change of Δk_eff,max = 8.4 and 7.7, respectively, amply sufficient for an effective control of a fast reactor during all phases of the space mission. By a nuclear thermal thrust around F = 5000 N and a specific impulse of 670 s~(-1) at an hydrogen exit temperature around 1900 K, the maximum temperature in the drums rises to 1023 K, with 100 natural B_4C content in the strips, far below the m
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