I’m not sure that you will be able to make this work, for a number of reasons, but I’ll make a few suggestions that may help.
- Make sure that you buy plants that can survive on very low light levels.
- Plants need nutrients, but tap water often has many of them and fish food can supply a few others. To be safe, it might be best to dose a good quality all-in-one fertilizer at the lowest recommended dosing.
- Fish will die from too much ammonia (read about the nitrogen cycle). Plants can take up some of it but, with the slow growth of your plants, it may not be enough. A filter can remove ammonia and trap debris (which helps keep things clean). You can buy very small filters. At least monitor ammonia with a test. Seachem makes something called “Ammonia Alert” which hangs inside your tank so you can view it anytime. I think that, without a filter, you will have to make numerous water changes, on the order of 20%, several times a week, depending upon your fish load.
- Without circulation, particularly of the surface, it can be hard to maintain good oxygen levels in a tank. If you see your fish hanging around the waters' surface, that is a sign that they need oxygen. The other benefit of a filter is that it provides circulation. The heat from the heater will create some minor circulation, but it may not be enough to create a uniform temperature. I suspect that it will be enough, though, and fish will move toward it if they need it.