When I drive my head lights are dimming although not all the time, also the heat

Not sure regarding the battery. I just got the car in March. It seems to run for while and then will not start. It was happening monthly but now it happened on Sunday and today. I drove for 1/2 hour before I stopped for gas on Sunday and it wouldn't start. A jump started it. It was fine until today. I drove to work, started it twice due to the really cold temps(10 degrees) and when I tried to start it to go home it was dead. A jump started it. I left it run for an hour but when I went to start it after turning it off, after backing into my garage, it was dead again.

Replace the battery and have the charging system checked.