Does it mean air-con and air-purifier should be turned on at the same time for best comfort?
Of coz. The AC not only removes the heat, it also lowers the relative humidity at the same time. Else it gets all muggy, the humidity has nowhere to go, using a fan does not lower humidity (which when combined with heat as shown in the calculations above, it's a very bad combi).
The main issue is not only about the temperature rise in a closed room with 1 to 3 or 4 pax in the room. When the temperature rises in the room with heat sources like human beings/the TV/PC etc, maybe the walls/floors/ceiling/furniture would absorb a fair bit of the heat.
The humidity in the room would also rise (I mean we humans breathe right?), and that does not really go down.
Other than the much higher Heat Index temperature, a high RH% also makes you feel sticky etc.
I mean, heck, of coz you still can force yourself to sleep in a room with doors/windows closed even on the hottest and most humid nights in SG even in hazy conditions. I don't know, i mean some pax also posted during 2015 heavy haze season that they slept with their N95 respirators on.
Personally for me, i'd not want to live in such a hardcore way......
If the weather is like Chiang Mai (heavy heavy haze now) where it dips to 21 deg C at night then yeah......if the indoors humidity gets high due to people in the room and windows/doors closed then it's still alright coz internal temp would be maybe 25-26 deg C, like our rainy days humid nights condition.
I guess YMMV, your mileage may vary..... *shrugs*