I can't see anything wrong with your circuit, so I would assume a faulty component or accidental misconnection at some point.
Nano has decoupling caps just like Uno or any other board. They wouldn't work without them. Lack of decoupling caps does not cause overheating.
If what you show above is the complete circuit, you should be ok to run the Nano direct from the 12V supply to the Nano's Vin pin. Nothing is drawing any serious current from the Nano, so it's regulator should be ok. If anything was drawing more than a few 10s of mA from the Nano, then it's regulator would be in danger of overheating and your buck converter would be a better idea.