Sounds like the case has poor airflow. If you're using an old case, you're probably not getting sufficient airflow through it since they weren't designed with these monstrous graphics cards in mind. I say this since there is hot air coming from the back of the card, which should not happen if enough fans are pulling air out of the case.
Depending on your case, you can try to alter the air pressure in the case by adding more fans to the top and sides (if the case allows for it).
The airflow that I use in my cases is called Positive Airflow. What this comes down to is basically having more fans as outtake than intake. The fan at the front of the case stays as intake, while the fans on the top, back, and side are used for exhaust. Since there are more fans exhausting, air will get pulled in from the cracks and other open areas of the case (like the screen meshes some cases have in the front). If done correctly, you will be able to feel air getting sucked in from these places. The advantage of this is that air will constantly be flowing through the case, and no air will "sit" inside. The disadvantage is that there is a higher chance dust will get inside your case since air will be getting sucked in where there are not fans. I personally use this method and recommend it.
Or if you want a simple approach, add a exhaust fan to the top of the case. I had a mining rig without it for a while, and you could feel the heat radiate from the top. Now that there's a fan on top, the hot air gets pulled out and replaced with fresh air much better than it did before.
Of course this is all assuming that you have a case that can have fans added to it. If not, I'd suggest getting a case with good airflow. Cases are pretty cheap at newegg, and a lot have free shipping.