Cleaning your heatsinks will go a long way to making any hardware run cooler and quieter. if you notice random shut downs or the system running hot there’s a good chance you need to clean the heatsink. It’s a nice afternoon project depending on the make/model.
While you have the computer open more RAM and a quality SSD will make a world of a difference.
Just keep in mind how much you are spending vs the age and currently value of the hardware you are not upgrading. Not worth pouring money into a Core2Duo system unless your budget is tight.
And if you want to do a good job with cleaning your computer, get a small air compressor. While the cans of cleaner work ok, a small compressor does a way better job and can be carried to the machine. If you have a big one, that is even better.
I’ve found using a compressor with a shop vac nearby and running is a good combo. The compressor frees the filth and the shop vac sucks it in before it lands on something else (or it gets inhaled).