Depends. What size cooler do you consider to be "big"? What's the water temp? What's the air temp? What size are the fish?
If the water or air temp is >80° F I'd rather wait until things cool down in the fall. If I absolutely had to haul them in hot weather I'd use my 275 gallon transport tank and aerate with industrial oxygen.
Getting bait to the river alive is one thing. Getting fish to your pond without overly stressing them is something else entirely. You might get them there alive only to have them croak after you turn them loose in your pond.
