Heat and solar energy: Transporting heat?

I just came back from Hungary where we had 9-18 C and here in Israel we have some 35 C. Last night I could hardly sleep because of the heat. As I don't have air-condition in my "study" it makes it a lot more difficult to use my brain. So I work slower and for shorter time, mostly in the evening hours. All this in the beginning of October.

I am planning to install air-conditioner which will greatly improve my situation but I wonder how much relation does this have with the fact that most of the worlds wealth is accumulated in areas where the weather is colder? Sounds obvious. (Well, besides the long running exploitation, but that was probably already a result of the lack of development in weapons.)

In the colder countries we use heating to overcome the cold while cooling, mostly air conditioning to overcome the heat. In most cases we use oil and similar sources to overcome the heat created from the energy of the sun. Why don't we use more of the suns energy to make the hot areas colder? Why don't we help the countries with lots of sunshine to export that energy?

There is a map of the world showing natural resource - potential solar power and as I read on Wikipedia there is some work in the cooling department.

But I have a more brain damaged idea: I wonder why don't we just collect the heat from areas where there is too much of it and transport it to areas where it is needed?

For a long time I tried to avoid thinking - and louding my opinions - on subjects that are so far removed from my core expertise as I think my contribution to these fields can be a lot smaller than to the field of my choice and even there it is very limited. Now, my dear reader, you could experience the wasteful result when I neglect my long standing self censorship.