While GERD is not curable, per se, there are a lot of things you can do to cope with the condition. Most importantly, adhering to a GERD diet (you can find examples on the web), losing weight, lowering stress levels, laughing a lot, eating more low-fat proteins, and exercising will all help control the condition, in essence (though not in fact) making it "go away". For a short while, however, you may have to take medications such as H2-inhibitors (Zantac, Pepcid) or Proton Pump Inhibitors (PPIs, like Nexium or Prilosec). You may also want to visit a holistic practitioner: there have been a lot of good results using techniques like acupuncture to help control the condition. Finally, if none of that works for you, you can consider surgery for the condition. There are various procedures available, though none guarantees a solution to the problem.
The heart is not actually being damaged by heartburn. A more accurate term is "acid reflux" because acid is refluxing into the esophagus. When it causes damage to the esophageal lining, you get "heartburn."
Note that uncontrolled GERD causes a lot of damage to the esophagus over time, and if left uncontrolled can lead to conditions such as Barrett's Esophagus, strictures, and esophageal cancer, so it's best it be controlled.
NERD is also known as "Non-erosive reflux disease", and it's when someone complains of GERD symptoms without any actual acid damage to the esophagus.
Now, I'm afraid.
You see, I tend to eat a lot of foods that have been known to prevent or reduce the risk of certain diseases/cancers. For example, I drink one cup of coffee a day, and a glass a wine a week. Coffee lowers the risk of prostate cancer. Wine is for the heart. I eat wheat bread, which is high in fiber so that I speed up digestion in the large intestine to prevent colon cancer.
But now I can't eat any of these things because they're not good for my GERD. And if I don't take care of my GERD it could lead to esophageal cancer. So I'm damned if I do, and damned if I don't.