The pain from kidney stones can be very severe. So it could easily cause you to feel hot, sweaty and flushed. But simply passing a kidney stone should not cause a fever.
When someone is passing a stone or has a stone that is hung up along the urinary tract with a documented fever, my first concern is infection in the kidney (pyelonephritis).
Urine that is either all or partly blocked from flowing freely from the kidney, through the ureter, into the bladder and out the urethra is more prone to bacterial infection. That infection is harder to clear because the normal flushing action is disrupted.
Antibiotics alone may not be enough. A specialist (urologist) will evaluate the situation with a CT scan and/or a kidney ultrasound. Then he or she will decide if something must be done immediately to drain the infection.
Here are potential options: