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MB3 57a: A Non Jew Lighting a Furnace on Shabbos (276:4-5)
If a non-Jew added fuel to a pre-existing flame. What if he turned on a heater (or air conditioner) on Shabbos? What if it's only being done for a non-Jew?
If it's very cold or if someone is ill.
Tzarchei Mitzvah/tzarchei rabim