Insulate your membrane or choose a good sun
In this system, any heat would escape outward. If you have heat inside, the only way it can leave is through the surface. You said that the planet is enclosed in a membrane, so make that membrane insulated to keep heat from inside escaping to the outside.
Now, this will have the side-effect of not allowing any heat in either. So how can you keep the ocean liquid? I'd say your best bet is tidal heating. The idea behind this is that rotating around a big object will cause the liquid to move around, generating heat. Moons like Europa and Io have vast sub-surface oceans because of tidal heating, Europa even having twice the volume of water of Earth despite being smaller than our moon.
If that's not enough heat, you can always have some sort of heater to input extra energy into the system when it runs low on energy.
Given that, I think you could get easily large enough to thousands of species. If heaters don't work for your story, you'll have to make it small enough for the sun's energy to heat the whole thing. I can't give you any specs on this, because it depends on the sun. You'll need to be as close to the sun as possible, but you have to be outside the Roche limit, or your planet will break apart. So brighter sun = more energy that can get to your planet, but that usually is paired with larger sun = the further away your planet has to be, allowing less of that energy to reach it. You'd want the brightest yet smallest mass sun possible to get the largest planet.
The next part of the answer will deal with the assumption that you're using my first solution, because you'll probably want to go bigger than the sun allows.
Now here's your problem: How are these creatures getting their energy? There probably aren't sufficient nutrients in the water (okay, you said they put impurities in the water, but it'll have to be constantly replenished) and definitely no source of energy (unless you're also constantly throwing food in as well). Energy would have to come from the sun, which is blocked out by our insulation. If we removed the insulation, the inside might freeze, but at least energy is going into the system.
And really, even if your inside is liquid without a membrane or anything like that blocking the sun, it wouldn't be habitable to life. Deep-sea ocean life on Earth is only possible because of hydrothermal vents, which couldn't be present in a solely-water world. These vents input energy and nutrients into the system, because absolutely no light from the sun is reaching that depth.
So, in conclusion, the only way I know to have a large, 100% habitable planet is to constantly feed energy and food into the system or to have an ultra-hot yet very small sun. If that works for your story, great. If not, just make it a watery planet without having to worry about ice at the core or anything like that. That way you can have hydrothermal vents and stuff to keep the inhabitants alive. That's my suggestion. It'll also have a lower Roche limit than a 100%-water planet so it can be closer to the sun and get more energy from it.
I hope that helps you. If not, let me know and I'm happy to add anything you need to my explanation.