Thank you for your query,
During the sleep children in this age group they may develop terrifying dreams and night mares so this may be the cause for her racing heart and restlessness
Whenever you find your child hot check her temperature by a thermometer, if the temperature is more than normal you can say child is having fever
, if it is normal nothing to worry.
3 year old child usually requires a nap in a day time for 2 hours.
Still you face problems with your child consult your Pediatrician