Great story. Keep up the good work.

Another great "Heat" story. Keep em coming!

I am going to be kind and assume that this is your first fan fic. If so, this kind of story is pretty much where we all start out - characterization problems, stilted dialogue, faulty timing of the action, overdone plot line, and a completely unrealistic heroine (aka, Mary Sue) who dies nobly and is eulogized by the adoring masses.
The good points are that you do have a pretty good grasp of grammar and have the potential to become a much better writer. Listen to the characters speak, and try to hear the rhythm that they use. Ask yourself, "Is this really how a professional police office would behave?" These guys are tough cops, and they wouldn't knowingly let someone who is dying of cancer go out on a dangerous investigation.
This is a nice start to learning the craft of writing, and I'll look forward to reading more of your work down the line.
P.S. Do you have a beta reader or an editor? They are a big help when it comes to catching potential problems with characterization and plot.