Temperature itself does not affect the speed of light - remember that space is freezing cold, and light moves through it just fine. So warmer temperatures don’t do anything with time.

If earth suddenly gained a bunch of mass, that would change things up as gravity would increase. However, we wouldn’t really notice, as everything would speed up more or less the same. We’d have to compare ourselves to someone in a system where time moves differently in order to notice.

no more or no less than the mass of the earth changes and our relative speed changes.

Could our day/night duration change, well that is totally different than Time changing.

No, But the melting of the ice caps would make the earth rotate slower (think rotating ice skater spreading her arms), thereby lengthening the day.

No. What?

No.

Also it wouldn’t matter to day to day life because time is based on your frame of reference, and you’d be inside the frame of reference so it would feel exactly the same to you.

Think about what it means for “time to move faster”. If you’re within the faster timestream, you may not even notice, unless you ascribe to one of the more interesting metaphysics which theorize that consciousness can exist outside of time. But if you’re within a different timestream, you may notice the affect timestream speed up or slow down relative to your own timestream.

Now, I’ve read your potential reasons why temperature may affect the passage of time. As to E=mc², the energy is not increasing, but more potential chemical energy is being turned into ambient heat, eg. by burning fossil fuels. Super simplified, ofc. but it’s not a case of energy being added to a closed system.

stares intensely at hand

What led you to this suspicion?