There are industrial PCs made expressly for this type of situation. They are typically rack mount, but I've seen desktops before. The cases have filters at all air entry/exit points. Where I work, some of the machine controllers are vendor-supplied, and have cases like this even though they're not really needed in our environment.
Over a decade ago I worked a job where I did Point of Sale systems support. The PCs were mostly made by NCR, ran Red Hat or SCO UNIX, and ran a slew of dumb terminals and printers through a serial terminal server box. These PCs had an enormous heat sink on the processor, which was fanless. A lot of them had been running 24/7/365 for 10+ years. They were nearly all located in the restaurant kitchen where the temp could get up to over 100F in the summer. (restaurants are not known for great climate control in their kitchens)
Usually I would find that the power supply fan and case fan had long since stopped turning, and the fans and some internals were coated with a think layer of sticky brown goo, from ingesting the greasy vapors in the kitchen air. (Imagine what it must have been doing to the lungs of workers over time) To their credit, NCR built a heck of a reliable box. Even with all this, I only ever saw 2 motherboard failures. One from natural causes, and one from a mouse living in the case and defecating/urinating on the system board until its urine eventually corroded through one of the traces that ran the PCI bus, stopping communication with the rest of the terminals. (the machine was still running) That one was such a biohazard I pulled the drives and the rest went in the dumpster.