Well if you've got it on or next to a heat register that could be heating it up.. or your thermometer could be wrong too, especially if you're using one of those stick on ones.
It's really important that tanks be kept on interior walls, away from exterior doors, windows, and vents
of any kind. They will cause temperature swings and heat and cool things unevenly.
Cycling takes up to 2 months and requires a source of ammonia to feed and you should use gravel/subtrate of some kind as well. http://www.bettafish.com/showthread.php?t=47838
. Low ph and low temps can stall your cycle too.
It needs to be moved away from the heating vent, and you should use a glass in tank thermometer to monitor temps. Unless you're keeping your house 80F+ consistently (no dips at night) he needs a heater. What size is your tank?