A heatsink has never been required for any 386SX processor in the history of ever, so no, leave it be.

386SX at 16MHz is probably an early Intel? These do run hotter than AMD chips and later low power Intel ones, but should not reach 75C or so, and this is still safe. That being said with zero airflow in the case everything will be cooking itself, slowly but surely, and while that will not kill any chips right away you will be stressing and aging them faster. I would worry about the VGA card and DRAM chips. Preferably add a small, silent fan to the case (and run it on 5V or 7V as well). Any airflow, even very slow, is going to improve the temperatures.

Yeah I was not planning on putting anything on top of the CPU itself. But was considering a fan for the case as Deunan recommended. I'll make sure to integrate a typical PSU-fan-sized one near the back. Cheers!

386SX have been used in very cramped systems by OEMs before, built into early laptops with as little as a quarter inch of airspace over them, and the whole machine had just a few vents maybe for convection cooling. Some had small fans, but I think it was more for the screen inverters and the hard drives making heat. In chassis where the CPU was kinda isolated and the HDD etc seemed mainly to dissipate through a metal frame they didn't seem to bother.

However, packing a machine with VGA, network, sound etc, the watts will add up and it's for the sake of those that some minimal airflow might be a good idea. You really don't need much though, and if trying to keep it quiet, find a case fan that spins on 5v and just let that twirl.

That system is before heatsinks really became a thing for processors.

You could stick a passive peel and stick on it if you wanted but it isn’t really needed