Is it a good idea to include thermal fuses in a DIY 3D printer design?
Whether you should use a thermal fuse or not depends on what other safety measures you've taken. You can't look at the safety features of a printer in isolation, you need to look at what other measures are in place.

The main fire hazard in printers is unfortunately (still) the fact that some manufacturers use underrated connectors on their boards, and that some users put bare wires in screw terminals or use inadequate torque when tightening terminals. As the wire works itself loose, it starts arcing and burning the connector. A thermal fuse does not help in this situation (unless you place thermal fuses near all of the connectors, which is impractical). Instead:


Properly tighten screw terminals, check them, and consider using proper wire termination (crimp lugs).
Use strain relief on wires. Make sure wires don't rub against anything, and guide them so they do not bend in a tight radius. Since the extruder (or print bed) is constantly moving, those wires are subject to fatigue.
Make sure connectors (especially those for the heated bed) are rated for the current running through them, and solder wires directly to the board if necessary.


Using a regular fuse may protect against wires shorting against each other should their insulation be damaged. Fuses are usually already integrated into the main board.

Most firmwares include some variant of thermal runaway protection, a feature that monitors the heaters and shuts the printer down if it notices something gone wrong. This protects against:


The thermistor coming loose/reading incorrect values/etc...


but not against:


Bugs in the firmware itself
Failure of the MOSFET


Most printers use MOSFETs to switch power to the heating element. Unfortunately, when MOSFETs fail, they usually fail closed (i.e. conducting). This means that, even if the firmware detects something has gone wrong, it won't be able to do anything about it. Solid State Relays (TRIACs) can fail in the same way.

To protect against this, mounting a thermal fuse (or resettable bimetallic switch*) on the heated bed may be a good idea. However, thermal fuses with ratings up to the operating temperature of a hotend do not appear to be available so this is not an option.

Attaching the fuse physically to the part it is monitoring is the most reliable, but for instance with the hotend (if you wanted to protect it all) this might not be feasible to the high temperatures involved so you'd have to settle with monitoring the air temperature close by.

Also consider thermal balancing. A thermal fuse is unnecessary if the component can not overheat to begin with. For instance, most MK2 heated beds struggle getting up to even 100C, so even with a shorted MOSFET they present no danger. However, if you have a powerful high wattage (mains-powered) heated bed, you should definitely install thermal protection.

E3D supplies their hot ends with 25W, 30W and 40W heaters. The 25W heater is the safer choice, since it limits the maximum temperature the hot end can get to, while with the 40W heater you can reach higher temperatures (and reach them faster). Barring a very unlikely scenario in which simultaneously (1) the power supply fails and starts supplying excessive voltage and (2) the MOSFET and/or firmware fails, a heater that is sized appropriately to the load it is driving can never pose any danger.

I don't think it's common to install thermal fuses on steppers, stepper drives or the power supply (which should have its own protection). For every possible location to place a thermal fuse, you can probably think up a failure mode in which that fuse would save the day, but at a certain point it just becomes overkill. The stepper drivers would likely burn out well before the steppers would get hot enough to pose a threat, and overheating of the stepper driver would probably (violently) destroy it but afterwards it should not pose any threat.

Axial v.s. radial does not matter, just use whatever is convenient for your situation.

* Note that some bimetallic switches short one of the leads to the (metal)
 case when tripped, which poses a danger, especially with mains-powered heaters.