All well said. Indeed, stepper motors run HOT by design. They are cheap and offer cheap controls -- pulses -- with no need for feedback (i.e., if all goes well). But there is no free lunch. You will "pay" for the low price elsewhere.
Stepper motors exhibit intrinsic holding torque (detent torque) that makes a motor "snap" into one of its 200 natural equilibrium positions. But what if you want to stop a motor somewhere else? You will need to pump in current in order to fight the detent torque just to keep that position, even in the absence of any external torque.
How do you make sure that you have enough torque if you don't know how much torque you need and if you can't detect when you don't have enough (no feedback)? Well, you pump in [ten times] more current than what you really need in a hope that it will cover your worst case scenario.
You can see that a lot of stepper motor current is wasted, and it is wasted in form of heat.
How hot is hot? 50C is not "really hot" for a human hand, and definitely not too hot for a motor. I have handled components at 60C+. Not pleasant, but definitely possible. I suspect chefs touch 150F pots every day. In my experience the point of "no touching" is about 70C (160F), but obviously different individuals have different tolerance to pain.
But when it comes to motors, as @Muzzer pointed out the standard specs can be as high as 180C (max in class H). I have designed motor stress tests running class B (125C max) motor windings at 170C+ (those were expensive Maxon motors for critical military applications; may not fly with your $15 stepper). As a matter of fact my Maxon motor rep told me they offer motors running at 240C (464F). Now
that is hot.
Back to Earth -- you have a CNC machine to build, your motors may not have a spec'd max winding temperature, and even if they had, you don't plan to invest upward of $500 in a FLIR camera to check the temperature while they are running. My [very unscientific] advice is this:
1. An open-loop stepper system design is too messy, with way too many unknown parameters to consider doing anything analytic -- forget that.
2. Your best bet is to duplicate (or start with) someone else's properly working machine
3. If you have a unique design -- play with the settings until you get to a point where a motor reliably does not [appear to] lose steps
4. Finally, if you can touch a motor with your finger for 1 second or more, you are in a really good place.