This is normally a case of the furnace overheating...shutting burner off (and thermostat power)...it cools...and everything magically comes back on. This can be as simple as a dirty filter....or in the case of a Carrier, a bad circuit board turning power ogg to blower. Check filter first...then see if when stat is blank if blower is still running or not.
I am just going by the make/model...the fact they had numerous issues with the blower function from circuit board, and your symptoms.
It is a very common occurence with that unit...but without a meter to test I am going by experience.