If it is not a problem that happens often it will be a big inconvience for you to diagnose. Usually what I have people do is disconnect the wall button wire from the opener head. This eliminates the wire and button as potential causes. If the problem goes away then you know you have a shorted wire or wall button and can take it from there. If it does not go away then I would erase the memory in the opener or reset the dip switches (depending on how old it is) and see what happens. In rare cases some else has a remote that will open your door and this eliminates that as cause. You could have a remote going bad and don't know it so another option would be to take the batteries out of all the remotes, if it goes away then you have a remote problem.

If the opener is 20 years old I wouldn't mess with it, I would just replace it, unless you want to wait a year and go without a wall button or transmitters to see if the problem ever comes back.

If it comes back in the cold weather it could be the heating system triggering the door. Older openers have pins to change the code, you could try that.
Ron