Let's go back a few steps
Question - Why do you think you need a 3A regulated supply ? What is your actual load ? Just because the power supply can provide 3A+ doesn't mean your regulator has to be rated at that figure. If 6 volts meets you back-up needs than "losing" 12.5 across a linear regulator is a shear waste of power (12.5 x 3 = 37.5 watts). If you really need 6 or 12 volts (you seem to be a bit mixed on voltages) then I'd suggest a switched mode regulator that offers over 90% efficiency with very little heat.