I installed I8kfanGUI, a handy little program for monitoring Dell Inspiron, Latitude, and Precision laptop temperatures, fan speeds, and CPU speeds and loads. It allows you to manually control the speed of the laptop fan; I used this to max the fan speed, hoping to bring the processor core temperatures down to something reasonable. Under high load, temperatures were still staying as high as 85C, and the laptop's performance was suffering as Windows automatically 'throttled' the processor speed to keep the temperatures from continuing to increase.
Time for more drastic measures. Using this helpful guide to disassembling a Dell Inspiron laptop, I completely took the machine apart. Inside: giant dust bunnies, completely clogging up the heatsinks at the end of the heatpipes that cool the CPU and GPU. These could not have been removed simply by blowing some canned air through the external vents on the laptop; I had to use tweezers to dig out them out. The fan was still spinning, but the air wasn't getting where it needed to go to keep things cool.
Success! I reassembled everything, fired it up, and the load temperatures were down into the 60's. Still pretty warm, but no CPU throttling and no performance loss.
Loss of computer performance over time is NOT normal. If a fresh install of a stable operating system doesn't solve the problem, heat management may be the issue. A computer is just like any other piece of machinery, and a little routine maintenance can make all the difference. It can be a real pain to take a laptop apart and put it back together again, but an hour of effort can make it usable again.