What was found
PHX - INFLIGHT RED NOSE GEAR LIGHT ILLUMINATED WITH GEAR UP. ALSO TAIL COMPARTMENT HIGH TEMPERATURE LIGHT ILLUMINATED FOR A FEW SECONDS ON CLIMBOUT. RETURNED TO PHX AND LANDED WITHOUT INCIDENT. FOUND LEFT HAND SENSOR SWITCHING ON AT LOW TEMPERATURE. REPLACED NOSE GEAR LOCK SENSOR AND CLEANED LEFT HAND AND RIGHT HAND SENSOR CHECK VALVES. SYSTEM GROUND CHECKED NORMAL OPERATION.