hp 550: Need help upgrading bios for core 2 duo to run win 7 64 bit

[ironrockinghorse]

I'm a photographer and i use photoshop lightroom extensively as part of my workflow. Unfortunately my desktop workstation just burned out it's motherboard in the middle of an assignment, and I'm not able to buy a new one till probably next month.  I have an old hp 550 laptop,  running on a core 2 duo processor. It was originally installed with 32 bit XP, but to run lightroom 5 it needs to run windows 7 64 bit.

I went through the Microsoft upgrade advisor instructions,  and it works great. Until you start Adobe 64 bit multi-threaded software (i.e. lightroom, premier).  After 15 minutes it over heats and crashes. Then i have to wait 30 minutes before it's cool enough to boot up again. I've got over 2000 RAW images to sort and edit (some requiring extensive edits) it is very slow and frustrating to have to shut down between each photo.  

From the system specs and the requirements necessary to run lightroom, it should handle it no problem. The core 2 duo is on the extreme low end but still fits the specs according to adobe. A computer whiz friend  suggested that overheating could be from the out of date bios. I realize this is not the machine to use long term, but i have to make it be able to make it work for the next two weeks.

I'm behind on this assignment, have another Friday and another next week. At this rate I'll never finish. I've built computers before,  but I've never dealt with modifying or updating bios, and I'm having trouble finding the right info and the hp website is less than helpful.

So what i really need is this.

1- what bios version is necessary for running windows 7 64 bit on a core 2 duo

2-I've never done this before and was told if done wrong it will likely render the laptop useless.  So I'd like detailed instructions on how to do it, if i may.

3- i was told the bios update may make a RAM upgrade past the current limit possible.  Is this true? If so it would help.

4- finally do you fine folks think this will actually work, or am I wasting my time and completely screwed?

Thanks all for your time!