You don’t need hot water, it just makes stuff more soluble faster, is more pleasant to wash with, and makes rinsing off the soap WAY faster.

Also, if you rinse off your dishes as soon as you’re done eating, or soak them in hot water, you barely need to scrub.

So, you don’t NEED hot water, it just saves a ton of time. I spend maybe 20 minutes a week total doing dishes. Having a dishwasher helps a lot, too.