The scaling can be tested by simply taking a tablet and putting the UI scaling setting on the maximum. To take it one step further, you can Teamviewer-in with your phone and test how it feels on a small screen
BTW people misuse the term "liquid cooling" quite often. Liquid cooling means a pool of water, a pump, and a fan cooling that pool. It cools the water, and the pump pumps it through pipes touching the processor(s). That's impossible in a phone.
There's also vapor chamber, which helps the phone stay cool for a bit longer, because the liquid inside takes away some heat. But when the liquid heats up, the phone takes longer to cool down, too. So, if the processor is always running hot, it won't help at all. However, it would help if we can find a processor that heats up only sometimes. Maybe Atom? There are 8" Atom tablets with plastic bodies, and they run fine, so maybe those CPUs could be cooled down enough in a 5" phone made of aluminium.
However, the battery problem remains. I really see no way to fix this with current technology. There are really great new battery technologies around, but they're still only available in labs. Noone is mass-producing them.