dimension 4700 cpu/fan behavior

I realize dimension 4700 fan behavior has been discussed ad nauseum  on this forum but I haven't  found a post that addresses the next step.

After years of being irritated with the CPU fan accelerating whenever the CPU usage shoots up(and it increases at the slightest function such as opening another browser window) I thought I would see if it could be corrected. I concluded that fan speed is related to CPU usuage and thought the thermal paste would be the issue.

I replaced the Artic Silver 5;tined the cpu and heatsink and placed a small amount on center of CPU.No change.

I opened the case and set a small fan to blow into the system and that made no difference.

The system is running 3.6 Ghz pentium,  4MB ram and either Win XP sp3 .Other times I experiment with a Linux distro and that makes no difference

Is there anything else that I could do or is this simply a limitation of the 4700?