CPU and Case FAN spinning to fast

Are you positive there is no "power management" or "pc health" section in the BIOS that would allow the system to monitor cpu temperature and adjust the cpu fan speed? It would be very unusual not to have that option.

What are the cpu core temperatures??

I checked the BIOS three times but I'll jump into it again. It's a Gateway and its about two years old. It's at our shop right now so I don't have the model number with me. The only option I saw for the fan was under the Power section and it gave "Disable", "Never" and "On Next Boot". Again I'll search everywhere one more time but I think it's a very generic BIOS and the fan is probably controlled with a Chipset driver maybe from Intel? I am going exhaust that area as well. I believe there could be one more program from Intel that I can download. Otherwise I'm lost with this? I don't believe a fan controller will be the answer either? Something else is causing this.

Is the BIOS recognizing the CPU correctly?

I got an answer but it was unexpected and everyone answering my question was on the right track. As I mentioned, I installed an Intel Core 2 Duo E5300 processor on an Intell motherboard that had an Intel Core 2 Quad 6600 processor. I think I left the next information out of my question...and I am sorry for that because it may had made a difference with a diagnosis. When installing the Intel Core 2 Duo E5300 heatsink/fan, I quickly realized that I needed to remove the posts on the motherboard so that the heatsink/fan could fit over the processor. I have typically used boards that have always had screw posts so this issue didn't come to mind until after the fact! I removed the motherboard so that I could remove the bracket on the back of the board in order to remove the posts. However, there were these "clip" rings that looked like they would "snap" into the bottom of the screwposts holding the screw posts into the bracket on the board. I didn't have twisers to remove these "clip" rings so I opted to place the old fan back onto the new processor. I figured, if the started running and the PC came on, it was the processor that died, not the fan and I definately got an answer to this issue. Thats when after turning the PC back on after plugging connecting the motherboard back together was when I heard the fan run as SUPER SPEED! The answer was the fan. I finally got the new fan onto the new processor and it runs at normal speed. Oh and yes, I did find the BIOs settings to control the fan speed. I tried that first and that did not slow down the fan. Strange? It was as if the heatsink/fan was proprietary to the chip? I don't know if that is possible per manufacturer? This is a two year old Gateway PC and was the first hardware I had removed out of it. So everything was setup by Gateway.

Anyway, thanks for everyone's efforts. Again, yes I found the BIOs settings and it was a fan issue but I needed to remove that bracket and put on the heatsink/fan that came with the processor. And it now works.

I have never heard of a fan that is tied to the CPU for control in that way. However, there's another thought. Basically you used the heatsink / fan combo for your old CPU on the new one. That may mean that the tight contact necessary for heat removal was not there, and the CPU actually was running hot and needed more cooling.

@Paperdoc...that could be possible? However, by putting the original fan on the new processor, the threaded posts were being used which should have allowed for the necessary tight contact for heat removal. However, I did put a standard dot size (might of been a bit more) amount of thermal grease on the center of the processor and maybe it did not spread out enough? The new heat-sink/fan had thermal grease applied from Intel in a geometric pattern.

Best practice I have learned is to whenever and however possible, use a new heat-sink/fan when replacing a processor.