If the check engine light is turning off, then you have an intermitent problem that is only occuring when you first turn the car on. Everytime the light goes on the diagnostic trouble code is stored in the computer. Either while the light is on, or after have someone scan the computer and see specifically what is going on.
Since its not flashing, or staying on, its either something related to start up, or secondary, like an emission problem. Its impossible to tell you whats up, especially since it doesnt sound like its effecting the cars performance. It could be a faulty ignition coil, a loose or cracked gas cap, an exhaust leak, anything really. Its very vague when youre dealing with things turning on and off, heating up and cooling down. Go buy a scanner yourself, or have your local car parts place scan it. Once you know what it is, I can tell you how to fix it.
PS- if its older than 1996, disconnect the battery for the night, which on most cars will erase the memory, and see if it happens again. If its newer than 1996 dont, just go get it scanned, then tell me what it says.