Hi BoredOOM!
Welcome to the IFSQN 
This is a good question. CPU’s have fans which produce a constant flow of air through them. The purpose of this air is to act as a coolant, primarily to control the temperature of the power supply but also the motherboard, memory, hard drives etc. A hot environment will cause the fans to operate at full power and a dusty environment will block the flow of air and damage the circuit boards.
In my experience I can tell you that this kind of environment will certainly lead to failure of one component or another, and within a relatively short space of time. Fans are usually the first to go, then the power supply packs in, if not something else before it. Having said that some PC’s (particularly the older models) will just keep on going no matter where you put them, but this is the exception rather than the norm.
You have three options.
1. Don’t put a CPU in this environment at all. Since you are using Dot Matrix printers you are printing on multi-sheet documents so possibly despatch orders, delivery dockets etc. It depends of course on your exact requirement but you may get away with keeping the CPU in the back office and sending the print jobs straight to the printer over your wireless or wired network. You can pick up a network enabled wireless/wired print server with USB/Parallel/Serial printer ports fairly cheaply. And these devices will withstand a harsh environment much better than a PC.
If it is imperative that the workstation is right beside the printers then you could slot in a “Tablet PC” or “Thin Client PC” whose sole purpose is to send instructions back to the back-office PC to print the documents.
2. Option 2 is to get a CPU with a solid state hard drive (SSD). As I mentioned above the purpose of the cooling fans are primarily to cool the power supply, the purpose of the power supply is to power moving parts within the PC, like the hard drive, dvd drive etc. Take out the moving parts and you have a much lower power requirement, producing much less heat and therefore no need for fans. Again, you can pick these up around the place, albeit not as easily as a regular PC and expect to pay more. However because there are no moving parts whatsoever they will last much longer in the environment you describe.
3. Option 3 is to purchase a fanless cooling enclosure within which you can build your own PC inside of it. Such systems are typically the preserve of the most ardent geeks and gamers and I would recommend you avoid unless you know what you are getting yourself into.
If you are having trouble finding links to research the above please come back to me and I can point you in the right direction. I didn’t have the time to de-jargonify my reply as much as I would like to have, so if you need clarification on any of the terms and technologies etc just ask.
Hope this helps.
Philip.
