It would seem that this is dependent on whether an air conditioner on a time switch or thermostat would be accepted to be in use on Shabbos
This is based on the Mishna Brura On Shulchan oruch orach chaim 276,1
The Shulchan says אינו יהודי שהדליק את הנר בשביל ישראל אסור לכל אפילו למי שלא הודלק בשבילו - a gentile who lights a candle for the benefit of light for a Jew, it is forbidden to derive benefit from that light even for one whom the light was not intended for him.
the Rema adds -הגה: מיהו אם עשה אינו יהודי בבית ישראל מדעתו אין הישראל צריך לצאת אף על פי שנהנה מן הנר או מן המדורה -If the gentile lit the candle without permission one is not obligated to leave the premises even though he benefits.
The mishna brura then says
ואם הא"י עושה בע"כ חייב לגרשו מביתו מפני חילול
השם שיחשדוהו שעושה הא"י בשליחותו כיון שהוא בבית ישראל - If The gentile does it (lights the candle) against his will, He must drive the gentile out of his house because of profaning G-ds name that one would think the gentile is doing the Jews bidding in the jews house.
The Jew in Singapore / California is not doing any Melacha.
The Jew in Israel is not benefiting from the act of a gentile or a violating Jew for which it would be prohibited to derive benefit on Shabbos.
The only issue might be, that those present in the room who think that someone (e.g a gentile) has been told from before hand to switch on the air-conditioner when it gets too hot which is a Chillul Hashem as stated in the MB above, so if time switches or thermostats are accepted this will not cause any raised eyebrows and would be permitted.