Last night I turned up the thermostat and the furnace didn't...

Last night I turned up the thermostat and the furnace didn't run. I turned the switch (on the thermostat) off and then back on and the furnace ran immediately. It ran normally through the night. This afternoon I noticed it was getting cold in here...the room temp on the thermostat read 63, though the temperature was set at 67. Again, I turned it off and back on and it has run normally since. It is a gas furnace, forced air, and the unit is about5-6 years old. The fan turns on right away when I put it on "on" instead of "auto". When the furnace is running, it heats normally. Our thermostat is digital, but it is one of the round ones that you turn the face of it to adjust the temperature setting (not sure if any of this matters). What could this be?

it could be that the fan relay is sticking.
And for your thermostat, did you have it last year, or is it new?
Electronic thermostats need to adjusted for the furnace,

We were not here last winter. The thermostat does not appear to be new...I would guess it was installed when the furnace was (5-6 years ago). The furnace has been running normally for several hours now.

I would say its a sticky relay then.