In InAlAs/InGaAs double heterojunction bipolar transistors (DHBTS) with composite collectors, the reduction in current gain as the collector-base voltage is decreased (current blocking) is almost independent of temperature. This is in contrast to InP/InGaAs devices, where the blocking strongly increases as temperature is reduced. We attribute the temperature independence in InAlAs/InGnAs devices to electrons that are not thermalized as they cross the base, Our results have implications in the design of collectors for InAlAs/InGaAs DHBTs.