Hi, typically the printer that use 2 motors for drive Z axis are connected in parallel. This is not a good solution, the parallel divide the current. For that I made a serial adapter to increase the motors performance and use full drive current. In the video the howto …
Parallel dividing the current isn’t a big deal. Z screws have such an enormous mechanical advantage that your Z motors don’t need much current to work well.
Using the Motor coils as series should devide Voltage (Resistance double) as P=U*I this shouldn’t make a difference. Normaly your driver could deliver more current but not more Voltage - so parallel should be better ( you should have a seperate driver for each motor)
motor at full 2A of power has 3,5-4V
12V-4V=6V that the driver convert in hot
12V-4-4=2V less hot on driver
with one current of 2A you can drive the 2 motors … each in 2A
with parallel at 2A you can drive everyone to 1A
what is the best? 
you overload the driver so it can’t sustain the voltage. Sorry but this is crap - use two drivers which can bear the load you want. Also it is very strange that your Z-Axis need 2A.
But the driver is not converting that voltage in heat. Your driver just can’t deliver enough current for those motors. So putting them in Series will lower the total energy consumption - this is a bad design but if you don’t want to change it - it is probably the best you can do.
it seems your steppers have only 2Ω so they would pull (U/R=I) 6A on 12v - probably they are rated for 6v or 3v. There are also 12v Stepper with 35Ω these would only need 350mA
… 2A is example of max power … I take a screenshot
back to school if this is the best you can do …
oh i see you havn’t calculated your design or read any tech specs.
You are one of those try and error tinkerer - good luck then!
Your driver isn’t voltage limited in your setup, they are current limited. Your driver can take up to 35V but you aren’t anywhere near that. The difference in voltage on the motor and PSU isn’t dissipated by the driver like you describe, it uses chopper circuitry to regulate the current. A controller running at 24V isn’t necessarily going to run the drivers hotter than using 12V supply input at the same motor current.
@Jeff_DeMaagd chopper circuit is used to control the voltage not the current, not used in this case., The driver is not magic … check the datasheet … it use a normal h-bridge circuit with mosfet that works as switching mode. And the mosfet convert in temperature the voltage that it have on his d-s junction when it is on.
In this case the voltage on d-s junction is = power supply - voltage load - voltage drop on cable
On my old 3drag printer the driver hot over 90°C with 13.5V supply … but with 9V supply it works around 75°C without heatsink at 2A for phase (4A for motor) … from 3 years.
ps. new zonestar electronics connect the z motor in series on mainboard
OMFG. How about you stop pretending you understand how this circuit works. FETs are not expending voltage into heat like that. The choppers are doing exactly what a switched mode power supply does. FETs in switch mode either let no current through or are in full saturation mode which is very low resistance, barely consuming power. This is how switching power supplies are so efficient.
And the nuance is that it’s controlling voltage by controlling current.