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Equatorial islands are tough to beat in this respect. Kiribati is probably one of the leading contenders. Mean temps are the same every month of the year and the diurnal range is about 5 C. The difference between the record high and low is only about 14 C in many places in Kiribati: Extreme Temperatures Around the World- world highest lowest temperatures
There's probably a place in the world with even lower variation but you'd be hard-pressed to find it. It would probably be another equatorial island, but it could also be an equatorial highland climate with near-constant cloud cover.
I've been thinking it would be a low elevation equatorial climate that has near constant cloud cover and high rainfall throughout the year. The cloud cover would limit heating during the day and cooling at night. Water also takes a lot of energy to evaporate and releases energy when it condenses, so a very wet climate would tend to moderate heating in the day and cooling at night.
I think highland climates would have too much diurnal variation to count.