The pictures are too small to see. What is your MotherBoard model and what version of Windows are you using (32-bit or 64-bit)?
Looks like it will handle up to 48GB. But the question is...do you use even close to the 12GB you have installed now?
That's not a RAM issue, it's a cooling issue. What model Dell do you have? I'd look to either clean the dust from the heat sink fan, or add more cooling fans. Though, with a pre-built system, your fan options may be limited.
I have a dell presicion t5500 workstation... How do i know if i can add more fans.