If you tried to insulate your underwater home, making it water tight... wouldn't you suffocate yourself? Water does get stale, and run low on oxygen, creating a dead-zone, so wouldn't you want some flow of water to keep fresh water coming in?

Worse is that water has about 5% the oxygen content of air per volume (not counting H2O itself), and fish are only about 80% efficient at absorbing it.

The issue there, is you can't really insulate a home which has fresh water cycling through? That's going to keep it at the same temperature as the sea outside.

How could merfolk, or other underwater people, insulate their homes without suffocating themselves?