transmission cooler line size

[b5blueaar]

I just installed a transmission cooler that has 1/2 inch tubes and 3/8 barbed hose fittings for 3/8 rubber hose.
My question is: will the original 5/16 transmission lines be large enough to get enough flow for adequate cooling or should I upsize the lines to 3/8?

Dont want to burn up another transmission.
I also went to a 3500 stall TCI converter, so there will be extra heat to get rid of.

[Wrencher]

Larger lines wouldn't hurt, but the flow rate will be determined by the smallest hole the fluid has to go thru which is probably the fittings or passages in the case.

[Grancoupe]

Definitely want to run 3/8 lines.