***** NOT A TEACHER *****
Hello, Jason:
As the other posters have said, that kind of construction (kind of sentence) is FINE, and all grammar books accept it as EXCELLENT English.
Nevertheless, it is interesting, I think, to note that a (very) few writers are not comfortable with that use of "would."
Those (very) few writers seem to explain their objection this way:
1. This is 2014.
2. You are telling us about something that happened in 1962.
3. The use of "would" seems to say that you have the powers of prediction.
4. In 1962, you surely did not say to yourself: "It is 1962. I will not live in a place with a/c until 1972."
5. Therefore, one should say something like: "It was scorching hot. It was 1962 and I did not live in a place with a/c for another ten years."
*****
That is what those (very) few writers claim. But "everyone" uses "would" with NO problems.
James
P.S. Here is an excellent sentence from Michael Swan's Practical English Grammar:
"In 1968 I arrived in the town where I would spend the next ten years of my life."
I guess that those (very) few writers would prefer: "In 1968 I arrived in the town where I SPENT the next ten years of my life."