It's quite hot, let's head somewhere a little cooler.
Why don't we go inside where it is cooler?
In the first sentence, it is very informal and you are suggesting to go somewhere either inside or outside, as long as it is a place that isn't so hot. It's a suggestion and that person is able to turn it down or offer something else.
In the second sentence, it is a little more formal because it is posed as a question and this is only giving the option to go inside, which will almost always be less hot than outside.
There are lots of things you could say and do when it's hot and it seems there are two crucial factors which determine the type of comment you may make:
1. The location. Are you by the seaside? Near some snow? In a sauna?
2. The person you are with. Is this someone you can be naked with? Or a business colleague?
Anyway the above expressions may, or may not apply!
I am sweating, can we go somewhere colder like the shopping center?
To suggest going somewhere with air-conditioning is the easiest way to say that you want to go somewhere cold.
As I am in Japan now and I am not used to this heat, I often ask if we can go somewhere with air-conditioning. (We usually go to the shopping center or even just into the 7/11 for a couple of minutes to cool down!)
日本 
アメリカ合衆国 
イギリス 
アイルランド 
