Thermostat issue....maybe?

I have a 15 year old Trane gas furnace. The thermostat is a mechanical White-Rogers. When I initially turned on my furnace for the first time about one month ago initially the heat would not come on set to AUTO. After having the heat run a while on ON, I switched to AUTO and all worked fine for the week of cold nights here in NC. Temps rose to the mid 70's, so I cut the heat to OFF. Now temps have dropped to again and last night I turned my heat on and again AUTO would not work. I switched to it to ON and it worked just fine. Switched to AUTO after house warmed up. THis morning it was 55*F in my house. Turned furnace to ON to and house warmed up, however, warm air stopped blowing, just cool fan air. Today after work, I checked and the pilot light was out. I lit the pilot light and turned the furnace on, again works just fine on ON, but will not work on AUTO.
Does this sound like a thermostat issue or something else at the control box on the furnace.?? I was going to replace the old themostat with digital themostat to see if that fixes my problem. I also have a HVAC technician/repairman coming next week to check out the problem in case replacing the thermostat does not solve the problem.
THANKS!!!
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Get an electronic programmable thermostat because it will save you a LOT of money, and the side effect is that it will probably solve the other problem. Well, it's not going to keep the pilot from blowing out, but that's probably unrelated.

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