I don't know what to suggest to make your room cooler as it's quite obvious what's in my mind. I can only remind you that hot air rises which everyone should know as it's basic science so that explains why your room is hot during that time. Since you said after late nights your room will turn colder, have you ever considered setting a timer to switch off your air cond? Though by doing so, you need to switch on your stand fan all the time which is a good thing unless electricity is of concern.

If by 'better sleep', you mean good quality sleep, your mattress and pillow play a huge role in this, as long as you feel comfortable and very relaxed after you lay down, it's a good indicator to tell you they're suitable for you. And please make sure your water intake before sleep is less because you should avoid the need to pee at night as it's quite bad to wake up during deep sleep. This can be explained by the afternoon nap if you take a 10-mins nap, you will feel energetic, but if you take a 1-hour nap, you will feel drowsy.

If you mean easier to fall asleep, you should obviously avoid any kinds of light, especially blue light because if you don't notice, after looking at a blue light source compared to other lights with the same amount of time, phosphenes will stay longer when you stare at blue light source compared to the rest. Any light source will hinder the production of melatonin, so it makes you harder to get sleepy. I know it's hard to stop using your phone before sleep, so at least turn on the blue light filter with max settings and minimise the brightness if you haven't.

I couldn't think of more suggestions, perhaps you should ask more questions and I'll see if I could answer them?

Maybe consider getting those heat reducing sheets to place on windows? Otherwise, setting a timer that will switch your air con off automatically would be a good idea to cool the room earlier in the night

If you are not going to turn the air con on, then you have to train yourself fall asleep under hot condition.

I don't think it's an issue to wear them all day long as I'm doing it all the time and it doesn't affect my sleep at all. To be honest, I don't even wear glasses while I'm playing my phone on my bed before sleep  Of course, I set the brightness to be the lowest and the blue light filter to the max. Though, this is partly due to the fact that my body is used to it already and there's a term for this which is the circadian rhythm.