Just put the heater next to the filter outlet or use an filter with an integrated heater. Water flow should be higher than two times the tank volume per hour, so the temperature will be the same in both halves. Some shops, breeders and keepers of betta fish use this concept. however it has a few drawbacks.
1. No quarantine, If you share the water then you also sharing diseases. If you have to medicate one half of a the tank you will medicate both tanks.
2. Square shape. Usually tanks are rectangles. If you half it it will be a square. Your fish have less swimming room.
3 Many fish need large groups. usually its better to keep a big group of one species in a large tank. In the larger tank they have more space to swim. Plus teh can interact with more other fish. Many species have a minimum groups size, however they have a more natural behaviour in larger groups.
4. The cost per volume of the tank itself doesn't get much lower if you buy a big tank instead of two. Plus you have to install a perforated acrylic sheet in the middle. With all the other drawback its just not worth it.
I would use two smaller independent tank or a single large tank.. You can share a airpump between tank. and run air powered internal filter. I wouldn't exchange water between tanks.
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