I've never seen seperate core temp readouts before, but if that's the case, then one should almost always be hotter than the other since it will be the default for anything not dual core optimized. By the way, those temps look a bit high for that cpu. You should make sure you got good airflow through your case and think about adding an extra intake or exhaust fan (or both).

Yeah man, that's pretty hot. Is that readout from the computer just running with no programs open and stuff? Whats your GPU temp? You could try upping the fan speed(s). If I'm playin' a big powerhogging game, I usually take off the sides of my case and set a stand alone fan pointing into the case, that lowers the temp by a lot. I was playin' Mass Effect with my case on and with my internal fans only running at 50% (it's also summer and my room is at the top of the house, so it gets pretty hot) and I noticed graphical glitches happening, like weapon skins disappearing, so opened up my temp monitoring program, my GPU was at like 58 degrees and my CPU was around 50 degrees. I took off the side panels and ran a fan, and upped my internal fan speed, and went back to playing. I opened up my temp monitor again like 30 minutes later, and my GPU was running at around the low 40's and my CPU low 30's.

Nightblade, those temps are pretty bad. You could also download another program called Core Temp which tells you your CPU reading better than Speedfan and also tells the voltage.
AMD is known to run hotter than Intel chips but those temps looks pretty ridiculous, especially if that's idle. I wouldn't worry too much, but check the temperature with Core Temp just to be safe.

I had an AMD 2700+ that did that, so in the end I just bit the bullet and underclocked it.

That's pretty random. Even if you're primarily running single-core applications, you should never see a temperature difference like that. That's because a dual-core CPU actually alternates single-threaded processes between the two CPUs in order to keep the temperature down. Two things:

Are you sure that temperature measurement is accurate? Try some other performance monitor programs and see if you get the same temperature difference.

Has it always done this or did it start recently? If it's always done this, it's possible that you applied the thermal grease stuff incorrectly. With dual-core CPUs you generally want to just spread a line horizontally (or was it vertically?) across the chip since this will cover both cores better.

1. I take it you're not going to overclock, so a pretty cheap fan will do. I use a Zerotherm which was about $30 at the time, and it works for me. If I were you though, I would just purchase some Arctic Silver 5 and be done with it.
http://www.newegg.com/Product/Product.aspx?Item=N82E16835100007
It's just thermal grease, but it can easily lower temps by about 5-10 degrees. If you're not overclocking, you really don't need anything more than this.

2. Usually it's not the best solution for problems like these. If you have lots of fans, you won't notice a difference. In this case though, you could experiment with it and see if the temperature drops.

3. Core Temp is the more accurate one usually. I notice Speedfan doesn't read my temps correctly, it actually shows them lower than what they really are. I also notice more people use Core Temp, but Speedfan isn't a bad program. It doesn't read core temperatures as good though as far as I know.

If you want the most accurate results, use one of the programs that came with your motherboard driver CD or from the manufacturer's site. If it didn't come with one, and you have an nvidia chipset, you can check them by downloading nTune. Short of that, you could always reset your system right after a heavy load and go straight to the bios and look there. It also wouldn't hurt to go there If those temperatures are even close, they're way out of the average levels and are a definite cause for concern. The temps you're giving us are higher than my system has under full load, and I have a 6000+ x2 and two 8800 GTs all with stock cooling.

Are ALL fans working and moving air well?
How many case fans do you have?
How many blow in, how many blow out?
Is there a fairly unobstructed path from the intake to the exaust?
Is there enough room in the front/back of your case to ensure proper breathing room?
Is the case in an enclosed cubbord or other small shelf that's not letting the hot air escape as well?

I suggest you get one more intake and exhaust fan. Your case should have a spot for one on the front, and if you don't have a spot for the second one in the back, try getting a PCI exhaust fan for below the video card.