I have also found that the H310 generates a lot of heat but it works. Due to the heat it creates I stopped using it in favor of a general SATA controller card. Nothing fancy but it just works without a lot of power draw. See my system link in my signature if you are curious what I use, but I will not guarantee it will be supported for the next 5 years but it works with the current versions of TrueNAS, I hope it continues until I no longer need a NAS. I guess it depends on what you need your NAS to do.
But to answer your question, people have mounted small fans to the head sink or one thing I did do was directed air flow across the heat sink using a homemade cardboard diverter. I also have a High Air Flow case and I've modified it a bit and I now have fantastic air flow across all the components. by the way, that does not mean high flow rates and noisy, it's a nice slow and quiet air flow. If it were in my bedroom, i wouldn't be able to hear it, except for the drives clicking as they do their thing.