Probably a dumb question related to an oil change I got

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I got my first oil change on friday. I'm one of the people that have been complaining about the clunky 2nd gear change. I went with synthetic (based on this sites information)

Now, from what I know (which isn't much) this is impossible. But after my oil change my gear changes are a hell of a lot smoother. Like, noticably smoother. I wasn't even expecting it. I just got in my car and started driving away thinking nothing about the oil change and instantly was drawn to the smooth shifting. I wouldn't bring it up if it wasn't such a noticable difference.

I know the clutch has it's own fluid. So I don't see how the two can be related.

So my question is if the two can be related in anyway or if it's just in my head?

Also, is it normal for synthetic oil to heat up faster than regular oil?

Please be gentle if I'm being stupid. *Prepares lube*

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