Depending on the size of tank get one of those Hydor Mini Heaters 7.5 watt. I use these for my bettas and they are great, it will keep him at a comfortable temp and they are not expensive either.
He won't die if its to cold you just won't see much action out of him, but for overall health its best to keep them on the warmer side.
As for the filter, you don't need to put that in if you don't want to but do keep up with regular water changes for him. I do not use filters. Been keeping bettas way to long now and have done it both ways. I just prefer and see better results with no filter for my bettas but each to his own.
If the tank is a large one then you should put the filter on most of them you can adjust so the flow is not hard at all.
Hope this helps.