Say if it is lukewarm, has cooled down a little after coming out of the oven? That has no hygiene/health implications right? Because it is not raw beef. It has been cooked.
Make sure it is cooled completely. Putting hot things in your fridge can lower the temperature and cause food to spoil. Other than that, it's fine just to cover it and keep it in the fridge.
No problem putting it in the fridge. I just wouldn't put it right out of the oven in the fridge for a couple of reason - one being it heats everything else up and the second being it could shatter your pan.
It's all fine, my family does it all the time and if you wanna re heat it then just put it in the oven or microwave for a bit cause it wont make a difference to the meat. =)