Motherboard components to the left of the CPU and above the GPU are part of the voltage regulation cicuitry and can run quite hot, the 4 "chips" you mentioned are probably "chokes"..The DIMMs (memory sticks) are to the right of the CPU..The Dell XPS 8300 has an Intel P67 motherboard (made by who knows, you'd need to look on the board to ID it, maybe it's an el-cheapo made by ECS)..The case looks like it doesn't have good airflow as mentioned above, and maybe has low-speed fans too..I would not use SpeedFan (except for fan control), many times it requires alot of calibration to the offsets and sometimes reports non-existing temp sensors and wrong temps..It is NOT "Plug 'n' Play" so to speak and not for the novice user..For CPU core temps 0-3 (logical) or 1-4 (physical) use either Real Temp (preferably) or Core Temp, they will both read the MSR of your i7-2600 and automatically calibrate the Tj Max temp for you..Also as stated above, use EVGA Precision or MSI Afterburner to manually regulate the fanspeed of your GTX 570, or make an automatic fanspeed profile/curve..The GTX 570 can pull a max of 219W from the +12V rail, that's a little over 18A (need to look at the sticker on the PSU to see what the output is)..Use a PSU calculator to get a general idea of your overall system wattage requirements..I think a more powerful PSU should be on your list of things to buy..Prebuilt systems from Dell, Gateway, etc. normally put in the cheapest PSU they can get away with to run the system and then when you start adding things is when you start having problems..
I can't post links for some reason, so here's some URL's:
 
Real Temp:http://www.majorgeeks.com/Real_Temp_d6098.html
Core Temp:http://www.majorgeeks.com/Core_Temp_d5665.html 
PSUCalculator:http://extreme.outervision.com/psucalculatorlite.jsp
Everest Ultimate Edition (with free license key) might might work good for you as far as measuring temps and voltages, etc..Or EVGA Eleet might be better.
Everest Ultimate Edition:http://downloads.guru3d.com/Everest-Ultimate-Edition-4.6-Free-License-download-2298.html
EVGA Eleet:http://www.evga.com/eleet/
 
And also, welcome to the forums!

I would buy a better aftermarket case, maybe something like a HAF 912 and a better CPU cooler like the CM Hyper 212+. I remember upgrading my old Dell with a GTX 460 and even that card came dangerously close to overheating in that terrible case.