Vendors do this all the time for us in the cold climates of MN/ND. It really is the same packing method both ways in the winter time.
Quality styrofoam cooler box + Heat pack + properly bagged/cupped corals + FedEx not using the box as a football = good shipment of corals to the destination
This is assuming the spare space in the box is taken up by paper or non-biodegradable packing peanuts. Tape the heat pack to the top or bottom of the cooler, typically the top to prevent it from getting damp.
The trick with the heat packs though is air. They need oxygen to cause the chemical reaction in the pack. Whether you have a 24 hour or 40 hour heat pack they will only heat as long as they have air. So be sure to put them in the box right before sending, but let it warm up first so it is already warm when the box is closed.
Vendors can probably add more info to this, but that is what I have seen work in the past.