I don't think it really matters whether you clean it with hot tap or cold tap. Either way your running unconditioned water over it. If you make sure to clean bio in tank water so you don't kill bacteria, why would your mechanical be any different? I have 3 canisters on my tank. I have a rotation, every week I clean out 1 of the canisters. I rinse with whatever water feels good on my hands while I'm doing it. Warm-hot in the winter, cooler-cold in the summer. I guarantee I have plenty of bb in my tank.
trash the floss and use it for polishing