You don't need a filter, but a lot of people still recommend one. The only reason you wouldn't use one in smaller aquariums is if 1) you can't afford a filter/replacement media or 2) the flow from the filter is too strong for the Betta or 3) you simply don't want to mess with one. I'm assuming by "whisper soft filter" that you mean a Tetra 3i Whisper filter. Again, reviews on this filter are mixed. It's OK in my opinion, but nothing special.
If your house really stays at 78 degrees without fluctuating, then you can wait to get a filter. However, you might still get a thermometer to double check that the water is reaching and staying at 78 degrees. One of the benefits of an (adjustable) heater is that it keeps the water temperature stable, which is important for your Betta's health. Even if the water is warm enough, fluctuations that can stress him out. I recommend the Hydor Theo 25w heater which you can order online. It's small and would do perfect in your 1.5 tank.
For real v. fake plants, my advice is to stick with silk plants unless you are interested in learning about taking care of real plants in aquariums. Real plants are great because they will help filter the water of ammonia. However, you have to consider the light on your aquarium, make sure that snails don't hitchhike on the plant if you don't want them in your tank, and if the plant starts to die off then it is decaying in your Betta's water. Some other users here can recommend easy plants to consider if you want to go this route, but it should be personal preference for you.
^The water in the tank is not going to be 20 degrees cooler than room temperature...