The biggest problem may be your heat loss, but there may be some controls in the furnace having problems.
Most likely, by design the furnace should work like this: t-stat says it's cold, signals furnace. Igniter or intermittent ignition sparker comes on. Gas comes on, burner ignites. If sensing circuit confirms flame, the burner keeps going, other wise the "try to start" sequence is repeated. Once the burner is going, in a minute or three, the duct sensor feels that it is warm enough and turns on the forced air blower.
Depending on the age of your furnace, the exact type of ingnition and sequencing may vary.
You should not mess with this in a rented apartment. The landlord should have a technician check it out.