can someone give me advice please, my babee is sick and i must take her to the doctors... just recently yesterday afternoon i came home from school about 25 miles away and as i went to the gas station to fill her up i started to noticing a river radiator fluid beneath my car. i went home quickly, checked my radiator fluid container and it was above the max level about 2x it's max. i poured out the fluid until it hit the max level. I waited until the car had cool down to open the radiator cap and notice that all of my fluid has been drained

my question is.... is it because of the blazing hot weather it makes the car heat up faster and the radiator fluid just overflowed??? or is there something wrong with my temperature gauge or something? and one more thing is the fan suppose to be running once the car is on or just when it get's too hot? thanx