the fat is going to melt inside your stomach so it won't make a big difference. it might burn a couple of calories to heat up the cold food but cold or hot it will be the same temperature inside you.
is it bad to eat fatty foods cold? . say you're eating a fried chicken that you just pulled out of the fridge and you didn't heat it up. or say you have a fatty chili from the fridge that you ate straight out of the fridge. does the cold solidified fat from the food do harm to your body as opposed to the fat after being heated up?