I am sorry about your stepper motor driver. It might have been damaged because the current limit was set too high. I suspect something was wrong in your setup if you were only measuring currents less than 100mA. Can you post a picture that clearly show how you connected everything (including your multimeter)?
By the way, temperatures that are hot to the touch can still be safe for electronics, which can typically operate at much higher temperatures. (It is common for devices like these to handle temperatures well over 100 degrees C). However, in this case, it does seem like the driver was probably running too hot.
Firstly I must make you aware the A4988 boards I am using aren’t official Pololu drivers, I hope you can still find it in your heart to help me out.
I have two makes, one Sainsmart (black, the one that exploded) and on RepRap (blue, that I thought I had blown up but it turns out I haven’t)
I got a replacement Sainsmart one because I am on a tight schedule and I could get one next day delivery.
I am wiring both boards up exactly the same (per the PololuPres_V3.pdf)
The strange thing is, the RepRap one provides a 500mA at 12v when testing between the coil. However, the Sainsmart one provides just 20mA with exactly the same wiring. I have adjusted the potentiometer however nothing happens and I am careful to turn it too far incase it sets on fire too.
Even though those carrier boards also use the A4988 chip, they could have a different board layout, which would change how the current limit is set. So, I do not expect the same instructions we use for setting the current limit to necessarily apply to those boards. Unfortunately, because we are not familiar with the layouts on those boards, we cannot help you troubleshoot them very well. You might try contacting the manufacturers of those boards for support.