What factors promote honey's crystallisation?
The decisive factor is the plant origin of honey. The major components ( reportedly by some beekeeper books of my passed away father ) have ratio glucose : fructose about 1:1 to 1:1.7. Glucose reportedly crystallizes more readily, triggering fructose crystallization as well. So honey closer to 1:1 ratio has stronger tendency to crystalize.(**)
Aside of already mentioned factor of temperature, another factor is obviously the ripeness of honey. Lower water content in more matured honey means higher crystallization probability.
Seeding by already crystalline honey helps to trigger or speed up crystalization.
If crystallization is already happening, or if it is intended and desired, then stirring speeds up crystallization.
Seeding and stirring leads to many small crystals, what is applied during production of the pasted honey. This form is favourite one among people. It often dissolves faster then liquid honey during drink sweatening. It is also very convenient for bread spreading, as its flow is almost frozen.
Slow spontaneous static crystallization leads to big crystals, forming mechanically tough product, requiring big force to separate a chunk of honey(*). The crystallization rate, the size of crystalsfraction of residual liquid phase and physical properties of the product seem to be composition dependent as well.
If such honey is wanted to be liquid again, it is recommended to carefully heat it up in $\pu{40 ^{\circ}C}$ warm water bath. High temperatures affect the present probiotics and enzymes. Note that honey is along fermented milk the major source of natural probiotics.

(*) My father stored honey in 4 L flasks for home-made pickles. When honey was crystallized, we often digged it up by table spoons or forks. But unless they were very strong, like heavy stainless steel ones from Soviet Union, they had tendency to bend.
(**) Infamous one is larch tree honey. It has so strong crystallization tendency it often crystalizes in the honeycomb. It is not being able to be directly centrifuged out without honeycomb destruction.