Older gas furnace is short cycling
I have an older Sears "Fifteen" horizontal gas furnace (#867767840) located in the crawl space. Recently it has been short cycling, meaning it starts a normal cycle, runs for approximately 1 minute, stops for several minutes, then starts another 1 minute cycle. This repeats until the set temperature is achieved. Also, the pilot light has gone out twice in the past two weeks.
Filters are new, all vents are open, returns are unobstructed.
So, I first replaced the thermocouple. And the pilot hasn't gone off again in several weeks, but the short cycling continues. I then replaced the thermostat. No change. What other things should I check? I am thinking it must be either a leak in the heat exchanger, or a faulty limit switch. Any help would be appreciated.