I'm not sure I agree that Europeans evolved at a 'higher rate' than any other group.

Certainly Caucasian Europeans are different in both appearance and genetic makeup from the ancestral humans who arose in Africa, but Europeans are no more distinctive than other groups that have also diverged, such as mainland Asians, Pacific Islanders, other Caucasian groups (Indians, for example), or even modern Africans.

If we're talking about the actual speed of evolution, modern Africans provide an excellent example of rapid evolution: the gene for sickle-cell anemia. Individuals who are heterozygous for the sickle-cell gene (only 1 copy) are very well protected against malaria. But malaria and the mosquitoes that carry it only appeared in Africa in the last few thousand years. This is a blink of an eye from an evolutionary standpoint, but in that short time span the sickle-cell gene became common and now occurs at a high frequency in some African populations, providing good protection against one of the deadliest diseases on the planet (sickle-cell anemia only develops in homozygote -- individuals who have 2 copies of the gene).

While Europeans, like any group of animals, have evolved adaptations that help them survive in their environment, such as copious body hair and pale skin (which helps increase levels of Vitamin D production), these same characteristics make them completely unsuitable for different environments (Europeans' pale skin and low tolerance for salt stress makes them rather unsuited for life in sub-Saharan Africa). So I don't think we could say that Europeans are genetically superior, but rather that they are well adapted to their environment.

In any case, Europeans and their descendants have been at the forefront of technological innovation for much of the last few centuries (I'm thinking mostly of the industrial revolution here), and as you suspected, we can largely attribute that to environmental differences.

Jared Diamond discusses this sort of thing in an excellent book entitled "Guns, Germs, and Steel", which I highly recommend. Dr. Diamond suggests that European societies prospered greatly because they were able to take advantage of a unique combination of many easily domesticated animals and crops from the Asian mainland (cows, pigs, sheep, wheat, barley, etc.), and a relatively mild climate (thanks to the Gulf Stream and Atlantic Ocean). The combination of these factors led to a society with lots of excess food capacity, a move away from subsistence farming, specialization of labor, and an environment conducive to rapid technological and industrial innovation.