I had no idea either until fairly recently. https://en.m.wikipedia.org/wiki/Heat_pipe I repaired a laptop where replacing the paste didn't help, but replacing the pipes (or rather the heatsink assembly, which they're a part of) did wonders.
If you're already comfortable with taking it apart, it's trivial to replace. I think it's your best bet. You might even be able to get it directly from Dell since they also sell replacement parts.
For such an old laptop I'm not sure if I want to keep spending money on it, $15 to upgrade the ram, $10 for a new keyboard after I broke keys from taking them off to clean them, $25 for a new battery etc.
Even though it runs very hot it does seem to work ok, and I'm hoping to just buy a brand new $100 or so machine hopefully in the first quarter of next year, but we will see. I still may end up doing so though.
I think I would have to try and buy from Dell directly, as on ebay all the heat sinks were preowned, and may be no better than the one I already have.
If you're already comfortable with taking it apart, it's trivial to replace. I think it's your best bet. You might even be able to get it directly from Dell since they also sell replacement parts.