depending on which manufacturers data sheet you read
stepper motors run at 70C to 80 C (158 F to 176 F)
so too hot to touch is normal !!!
as long as the stepper driver is powered the motor will be run at full current
unless your stepper driver automatically reduces the motor current when its idle
this will help the motor to run a little cooler when its not being stepped
you will need to look into why the X axis is dead
John