The temperatures used to melt plastic in FFF printers aren’t particularly high, but they are high enough to cause damage when things go wrong.
Typically you’ll want to be using temperatures of 190 to 260 degrees Celsius at the hot end of your extruder in order to melt plastic to the right consistency for 3D printing. The temperature you choose is dependant on the type of material you’re using and the kind of finish you require.
Temperatures of this magnitude are more than enough to give you a very nasty burn. Luckily the hot end of most 3D printers is fairly small so you’re unlikely to cause yourself any life-threatening damage from burns.
However, I have burned myself many times when removing plastic from the nozzle while it’s hot, so be careful as it happens a lot and isn’t pleasant.
When printing with PLA you don’t really need a heated build plate but if you do the temperature should be relatively low. With ABS you’d typically use a higher build plate temperature of around 120 degrees Celsius.
Again, this is hot enough to burn you and the surface area is much larger than the extruders hot end. So, if you’re really worried about burns, just stick with PLA and you shouldn’t even need a heated build plate.
As with any electrical equipment, especially that which contains heating elements like your 3D printer, there is some risk of fire.
If you have ever seen the film Fahrenheit 451 you may already know that this film (or at least the original book) was named after the temperature which paper supposedly catches fire and burns.
This value is what we call the autoignition temperature of paper, which is the temperature which paper can burn without a flame.
However, there is no authoritative value for this as there are many other variables which affect this value, but realistically the auto ignition temperature of paper is around 30 degrees Fahrenheit higher than this.
So why are these numbers so important to 3D printers?