No pun intended sir, but i think walang koneksyon ang pagiging AT na Rio sa pag ooverheat at pagkawala ng preno since separate systems ang cooling system (radiator), braking system (preno) at transmission system. Correct me if I'm wrong though, but having the same cooling and braking system, an MT rio could have the same problems as you stated.
BTT: Pag long drives at pag matraffic, I prefer driving an AT.
Pag ako lang mag-isa, i just use my MT car so pede kong laruin at di ako mainip.