2002 BMW 325 Mystery occurence

One week ago, the coolant light came on. The level was low so I filled it. The next day, the coolant light went off but the service engine light came on. The car was running fine, and after a couple of days the light went off. Yesterday, very cold morning, about 20 degrees. Car started fine, but idled rough until it was warm, service engine light reappeared, but again, car was fine except for that early am rough idling. This morning, 20 degrees, car started but was VERY rough idling and thought it would quit every time I let off the accelerator. Tried to drive easy until it warmed up, but I had no power. The transmission seemed off, wasn't shifting smoothly at all and wouldn't go over about 40mph. Service engine light was on. Was afraid that I wouldn't make it to work so I turned it around and limped home. Mechanic came to the house 6 hours later. Car started with only a slightly rough idle, but otherwise mechanic said that it was fine in every other way. Engine temp heated up to normal, which rules out a thermostat issue. Shifting was normal this afternoon which rules out the transmission. This is really odd. Do you have any thoughts? Thanks!