An assembly consisting of a stack of three microchannel plates (MCPs) and a phosphor screen anode has been operated over the temperature range from 300 to 12 K. We report on measurements at 6.4 kHz (using an alpha source) and with dark counts only (15 Hz). Without any particle source, the MCP bias current decreased by a factor of 2.1x 103 when the temperature was lowered from 300 to 12 K. Using the alpha source, and a photomultiplier tube (PMT) to monitor the phosphor screen anode, we first observed an increase in the decay time of the phosphor from 12 to 45 μs when the temperature was decreased from 300 to 100 K while the decay time then decreased and reached a value of 5 μs at 12 K. The pulse height distribution from the PMT was measured between 300 and 12 K and shows a spectrum typical for a MCP phosphor setup at 300 K and 12 K but is strongly degraded for intermediate temperatures. We conclude that the present MCP-phosphor detector assembly is well suited for position-sensitive particle counting operation at temperatures down to at least 12 K even for count rates beyond 6 kHz. This result is crucial and an important part of ongoing developments of new instrumentation for investigations of, e.g., interactions involving complex molecular ions with internal quantum state control.