Hi. You can keep your betta without a filter and in fact a lot of them don't like much water movement (but other bettas LOVE surfing a nice water current--depends on what your fish likes). In a bigger tank (5+ gallons), a filter will help keep the water clean. As far as heat goes, it's best if you can keep your water temp between 75F-80F, and at a constant temp (not too much temp fluctuation). Otherwise, you'll need some heat source. Lately here where we are, the daytime (full sun) temp doesn't get much above 57F degrees (sorry, never learned celcius) so its either keep the room heater on all the time which would get too expensive or else find other ways of heating the fish without burning down the house.