Chlorine CAN purify literally tons water in less than a cycle!
You need to use a liquid reservoir, a more recent addition to the game. This interacts with its gaseous environment, including the antiseptic properties of Chlorine gas.
First, set up a flow of polluted water or sieved toilet water (or water that's been vomited or urinated into) into a liquid reservoir.
Once you've got a flow into the reservoir, use automated or manual liquid valves (preferably liquid shutoff) to stop the flow of infected water into the reservoir once it's slightly filled. This will give the germs time to die before more is added into the system.
From here, there will be germs in the small amount of piping coming off of the reservoir and into the liquid shutoff. This is unavoidable, as pipes do not interact with Chlorine to purify their contents. Attach a germ sensor within this loop, into another liquid shutoff. If any germs are detected, send the cleaned water one direction. If not, override the liquid shutoff and send them back into the purifying loop for the next round. From here, all dirty water is free of germs. I recommend doing even a third shutoff germ detection, to get any excess from pipes out of the output, just in case any slipped by the germ sensor filtering.
This whole process can be easily automated by timing it with a daylight cycle sensor. The chlorine room is relatively easy to set up, and can take a full input of 2 sieves, easily processing the entirety of waste water from a colony of 32 in a 6x4 or 8x4 tile room.
Although this sounds complicated, it's much easier to set up than a tepidizer, much more power-efficient, and it produces no heat or waste product outside of the sieve.