When computer heats I get blue screen

If the issue is truly linked to the temperature of your system, then there's not much point in troubleshooting the software you're running. I mean, granted you shouldn't be flogging your processors if you don't have to, but you will have to. Often.

It's kinda normal for FireFox to hammer your RAM, ditto for Flash and your CPU. This'll only get worse over time as more updates are released to "take advantage" of the "latest and greatest" hardware out there. However, your computer should be able to take it, so long as it's got not being suffocated - make sure it's got a decent amount of airflow, for one thing.

SMC/PRAM resets are worth a shot. Don't expect anything out of them, but you never know:

http://support.apple.com/kb/ht3964

http://support.apple.com/kb/ph6478

You may be able to control the issue to some extent by taking manual control over your cooling system. By default Apple likes to run the fans slowly, allowing the system to heat somewhat but reducing noise (form over function and all that); although they crank the RPM up when things start getting toasty, in your case it seems that's too late.

SMCFanControl allows you to enforce minimum rotation speeds, and also lets you track the temperature of a few parts separately (eg CPU/GPU/HDD):

http://www.eidac.de/

It's always fun to max 'em out for the first time on a system that's served a year or two. Don't mind the cloud coming out of your computer - that's the built up dust being shifted out, not smoke. 😉 Obviously, running your fans at full speed for extended periods is a bad idea (you'll wreck the bearings and the fan's'll be loud no matter how slow/fast they're going), but experiment with different levels and see if knocking, say, 10 degrees Celsius off your average temperatures helps.

I'm mostly inclined to blame your graphics card(s). I've noticed a lot of reports where systems with two cards will have problems when the system tries to switch between them - in some cases Apple's been able to patch these issues away, but I suspect in a good percentage of others the only solution would be new hardware.

On the other hand, you're not getting graphical issues - your "blue screen" sounds like Finder itself is crashing or something. Dunno. But since this is your model, have a read, see if it sounds relevant:

http://www.mactrast.com/2013/10/owners-early-2011-macbook-pro/

You could try preventing graphics switching maybe:

http://support.apple.com/kb/ht4110

And of course, Safe Boot is also worth testing out:

http://support.apple.com/kb/HT1564

Indeed. Anything's possible, but it's rather more likely to make things worse - in a "computer won't start up anymore" kind of way. Mavericks taxes your hardware more so than Snow Leopard.

For everyone who isn't in a position where they can afford to wipe their drive "just for a laugh", I recommend a full system backup - whether you think your computer may be in strife or otherwise. You're far from that position, so pin such a backup at the top of your troubleshooting "to-do" list.

Time Machine is trivial to setup with most any decent USB hard drive, and even if you've got a lot of files to copy the first backup can be performed overnight. Yeah, drives aren't free, but ask yourself how much time and money you'd be willing to invest to salvage your data if your system died tomorrow...

An update to Mavericks will not likely help your issue.