2005 Toyota Echo Intermittent coolent fan and cold sensor

I have a 2005 echo and I am seeing check engine lights intermittently, the coolent fan is comming on for about 2 seconds then the check light comes on. The coolent fan should not be comming on in the middle of winter right after I start it up in the morning. Also the cold light in the morning will go out after about 10 min of driving then come back on after the car is at operating temp.