We have a carrier furnace installed in 2010 that is erratically providing heat, and it never comes up to temp. It is displaying Three short blinks and three long blinks

Three short and three long blinks = Error code 33. (The Carrier fault codes are two digit numbers. The short blinks are for the first digit, the longs ones for the second digit.)
A 33 error code = "Limit Switch Lockout" (Check for a dirty air filter or possibly a blocked return air or supply air grilles)