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 B4C strips (with 20% B-10 and 80% B-11) and produce nuclear heat via neutron absorption in B-10. 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 similar to 50 kW(ei) in power phase. Reflector drums with 100% natural B4C 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 Delta k(eff,max) = 10.7% without a significant distortion of the fission power profile during all phases of the space mission. A reduction of the B4C in the strips to 20 and 10% would still allow a reactivity change of Delta k(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 it 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 B4C content in the strips, far below the melting point of beryllium. The maximum drum temperature is depressed to 663 and 519 K, with 20 and 10% natural B4C content in the strips, respectively. (C) 1999 Elsevier Science S.A. All rights reserved.