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We have a good relationship with them but we are curious as to how they must view us.Why is it okay for them to ask us to "work" during their Sabbath?
You can consider it a great kindness to be helping them out, just as any good neighbor would.
One story (probably apocryphal, and popularized by Leon Uris in his book, Exodus) says that King Christian X bravely promised to wear a yellow star if the Jews would be forced to.
The Sages say that having a friend is so important that one should be willing to pay for it!
This is a Talmudic principle, as derived from the Torah which states that on Shabbat, "creative activity should not BE DONE for you" - i.e. The only exceptions are: when there is a commandment to be fulfilled, great monetary loss, or a health-related situation.
Air conditioning is considered health-related, because if things get too hot, people (especially the elderly, etc.) could faint or be exposed to other dangers.