[trahana]

Its quite possible to have a small filterless tank. Its not at all suggested if you need it heated though.
I have a 2.5g tank that is all plants and a single betta. The water parameters are flawless and I change it once a week, about 50%, and vacuum the tank every other time. Dirt is okay. Dirt breaks down from both detritus worms and bacteria. Plants eat the nitrates, and the cycle is complete with new water every week. It takes Way more time and care to set up a filterless tank, and expect more then three months of daily checking of water and water changes every other day. If you have a filter that works with the tank, keep it that way. You won't need to worry as much.
For the heater part: Hot water rises while cold water sink, so if you don't have circulation you can have a huge variation in temperature in just 10g. So no heater if their is no filter since it can cause temperature shock.

 

[trahana]

Will there be a large variation in temperature in a small tank? Would an air pump counteract that? The issue with the filter in my 3 gal is that it’s REALLY big and the inbuilt light is killing my plants off. And I’m unsure about the ehiem minis flow? I feel like it will be too strong..

Can you do a sponge filter? That is a fantastic way to use an air pump and make it cycle friendly.

The depth of the tank makes the difference, I think anything over 5 inches of water needs circulation. Personally I stopped using heaters because I have a warm room, so I can do filterless tanks.