In August 2013, NASA powered up WISE again with a mission to look for asteroids headed towards Earth. How is WISE seeing anything given it's IR detectors are out of coolant?
In general IR instrumentation can work at higher temperatures, just poorly, in comparison when cooled properly.
Usually when designing an instrument with a known coolant lifespan it makes sense to ensure it can at least function (even if degraded in quality) after the coolant runs out.
Space can be 'cold' if managed properly. IR instruments like REALLY cold, which is hard to attain passively, but passive cooling is required anyway, to keep coolant use down as low as possible.