Does Pi 3B+ need extra heatsinks to run Octoprint?
Depends on how and where you use it. Do you live in the Sahara or do you plan to put your Pi 3B+ on your printers heated bed? Then some cooling solution would be advisable. But the 3B+ in a somewhat ventilated environment works without extra heatsinks.
Honestly, my Robo 3D has a little oven chamber in the bottom of it where the Pi lives. It requires heat sinks on the CPU/GPU of the Pi as well as a beefy fan down there.