Most rabbits are ok down to 40F at least, and colder if they have built up a winter coat and have access to a draft free nest area. They tolerate cold temperatures much better than hot. If he’s in the house and you’re able to live there too, you have nothing to worry about. My house gets down to 55F while we’re gone and the bunnies are fine. I would really only worry about an outdoor rabbit in a climate that gets below freezing.
Rabbits regulate their body temperature with blood vessels in their ears. When the ears are warm, it means your bunny is warm and trying to cool off. If the ears are cold, it just means that your bunny isn’t overly warm, and is conserving heat. So it’s totally normal for the ears to get cold when the bunny has no reason to cool off.
You can get a bed if you want, but it’s really not necessary. Some bunnies like them, some ignore them, some chew them up, and some pee on them 😛