Welll, getting your APM up is the best way to start. I strongly suggest you look at Odawgg's arsenal guide and especially read the part about Always Be casting. In short, make use of the action queue so that before you're done with your current attack, the next one is already lined up.
I did a cropepd sample of both our parses at 250 seconds to get a more accurate comparison.
We're the same on the number of Thermal Detonators, so you're using those on cooldown. You have more incendiary missiles than me, which unfortunately isn't necessarilly a good thing. I am a little lax with them at times, but I don't think I miss them that frequently, which means you're sometimes refreshing IM when the dot on it is still running.
Now for the big thing, I have almost twice as many power shots as you do, and 25% more rail shots, while you have more unloads than me. Here of course one follows another, more power shots means more rail shot procs, which in turn means more heat dissipated.
But the main thing to improve upon is to get APMs up and being comfortable with the tighter heat management that entails.