Damn that's a great entry! Moreover for your first entry here, that's even better, congrats!
The intro is a great plus! That reminds me of the talk "The Art of Screenshake" of JW, when he talks about adding some meaning to the game, and that's what you do with this intro, so it's like you're more into the game, and moreover your intro is funny!
What you did is well polished and complete, so I won't have too much to add about it, but I have few points in mind that you maybe would like to consider to improve it (or for future games).
- The first feeling I had was that the character moved a bit too slowly, that kinda frustrates me a bit ahah
- Another thing is that when you're playing the game, as a player you don't really focus on the UI, and the overheated bar stays the same color if it's almost empty or full, and so you don't notice you're getting too much overheat, you only notice it when you're already overheated and can't shoot anymore. So I guess having this bar flashing when you're getting too much overheat, or maybe changing the color, the players will notice it more easily.
- Another feeling is about the sound of the pistol, I would give it a deeper sound when it shoots, so that you've the feeling it's powerful and that you're being badass shooting with it.
- One of the point of the talk I wrote about previously is the screenshake, and I felt I was missing it in this game. Maybe you could add some when firing, or when killing an enemy, you'd have the feeling it's a bit more "alive".
- One thing I didn't really get was how the weapon was improved, I think it was like cycle of 3 different fire rates but not sure at all. It was kinda weird that after improving it, it came back to normal after some time. Maybe adding a bar which gets empty with the time could help to understand the improvement is not definitive (or a least if is like that currently in the game, but that's what I understood, sorry if I assume wrong :x ).
- And as you do a scoreboard, I discover one thing by checking out games during this Ludum Dare, that is Dreamlo.com . It helps to create easily online scoreboard, and there is an implementation of it available on the asset store (I didn't check it yet), and I was thinking of maybe using it for my next Ludum Dare, so maybe you'd be interesting in it! ^^
Anyway, great game you've made, congrats!
Cheers!