Air gap intake and heater hoses

I'm wondering if the 1/4" i.d. is enough flow to still be 'hot' by the time the coolant gets to the heater core? If it is I'll just use the 3/8" hole.

I am pretty positive I used 1/2" and 5/8" hose on mine. 5/8" hose on the water pump and 1/2" on the barb. You can find fittings with the correct threads for the intake side with a larger barb on the other end.