Honey should be stored at 50-70 Degrees Fahrenheit
Honey is similar in to olive oil and should be storaged between 50-70 Degrees Fahrenheit according to Max Shrem from Slashfood:
Similar to olive oil, honey should be stored at a cool temperature
between 50 and 70 degrees Fahrenheit. So, it's best to store it away
from your oven or stove. Also, it should not be refrigerated. Extreme
changes in temperature will spoil the flavor of honey.
Looks like this confirms that you may want to keep it in a cool place and away from hot temperature where it would cause honey to degrade in quality.
Shrem from Slashfood continues:
Do not store honey in a refrigerator or near a stove or oven.
Store it in an air-tight container.
Thus, choosing an appropriate container is an important part of the equation.
Penn State has a great article germane to this topic.
In the article, it talks mentions the crystallizing state of honey if it is refrigerated in no way it harms the honey at all.
Restoring honey from a crystalized form
I know this is not related to your question. But something you asked in the comments. Apparently, honey can be restored from it's crystalized form: placing it in the microwave for 20 seconds can restore it from a crystallized form.
Therefore, you can store it in the refrigerator and heat it afterwards. The downside is that if stored in the fridge too long it'll turn hard and sugary.
Proper Storage Container
Since honey has very little moisture in it it is difficult for microorganisms to grow. Thus, an airtight container is of utmost importance.
If moisture gets in the container it can be an ideal environment for mold and yeast to grow. Honey should be thrown out if it foams and smells like alcohol
Long Term Storage of Honey
Honey can be stored for long periods of time without any issue. Over time, honey will darken and intensify with flavor.