It should be fine considering sleep is one of the least-taxing things on your heart, it makes since for it to beat at an easy rate. Like others said though, some heart rates are way lower than that(mine can get about 35bpm, but I am an avid runner) and there is nothing wrong at all. If you feel uneasy though it is better to get yourself a 3rd opinion and compare that 3rd opinion to the closest similar of the first two opinions.
Above 30 is normal during sleep. Even lower in athletic individuals.
24 hour low (during sleep) is not the same as resting heart rate. It's far lower.
Start here:
"What’s a normal heart rate?
Similar to many other matters of medicine, the “normal” heart rate requires meshing a patient’s symptoms, or lack thereof, age, history, exam and sometimes an ECG. Young people, athletic or not, may be normal in the 30 bpm range. Likewise, despite what you read in the NY Times, a resting rate in the 100 range may also be normal...........
.........But the heart rate is unlike a lab value. It’s far more complicated. For starters, the heart is immersed in a bath of hormones, chemical messengers, pressure sensors and neural inputs. These moment-to-moment inputs provide critical information to the natural pacemaker, which we call the sinus node. Simple example are: adrenaline release speeds the heart rate, while firing from the vagus nerve (which occurs at rest) slows the rate. But it’s not that simple. Genetic factors also play a role in determining both resting and max heart rates. So does fitness and stress and temperature and a host of things."
http://www.drjohnm.org/2011/08/whats-a-normal-heart-rate/
Clearly, the normal rate varies among various people. The doctor on the page where I got the information emphasizes symptoms as being a part of the determination on whether a certain heart rate is an issue. You are symptomatic in being fatigued. In that light, being hypothyroid would cause a slow heart rate and the feeling of fatigue. I'm sure other imbalances in blood chemistry would as well. Did the doctors do blood tests?
Have you seen two cardiologists, or two Doctors that don't specialize in cardiology, or one of each. You can consult an Electrophysiologist (a doctor that specializes in heart rhythm issues) for a diagnosis if you have not already done so.
If I were in your position and have had two Dr's give you two different suggestions then I would personally seek a 3rd opinion and work off that. Maybe see a Dr that works somewhere thats pretty known for cardiac care.
http://health.usnews.com/best-hospitals/rankings/cardiology-and-heart-surgery
With that said though, I have read on people that have low rates and are not athletes or exercise. Fatigue can be from so many things so I would guess trying to eliminate all the other possible causes. Even not exercising (not saying you don't) can make you fatigue