In my experience, there are many factors at play.
Proof Higher-proof results in faster infusion. I once did strawberries in 150 proof vodka with sugar and it was intensely infused within weeks, and never really dramatically changed after that. However, you may need to dilute the product substantially to get something drinkable. (I almost always used the strawberry one in mixed drinks, but there was so much water extracted from the strawberries that the alcohol content seemed to perceptively shift lower). I would never use lower than about 70 proof liquor due to the fact that, after water from the infused fruit, and sugar additions are considered, you lower the overall proof, and the stability of the quality (and possibly safety) of the fruit comes in to question the lower the net proof is.
Temperature With sufficient proof, room temperature is just fine. High-proof alcohol has a preservative effect. The lower limit is probably a net 50 proof, after considering the adjustment effect your fruit's water and sugar content have, although food safety experts might recommend a higher number.
Sugar Less added sugar will require longer periods of infusion before you have satisfying results, especially with infusions that most people expect to be sweet (ume, an apricot variety frequently mistranslated as "Japanese plum", apricot, peach, etc). I can get satisfying results in 3-6 months with most fruits when I have high sugar content, but it may take 6-12 months to get a well-rounded flavor if the sugar content is low.
Material infused Herbal infusions, chilies (habanero is the one that I've tried), and so on obviously don't typically have added sugar, but their flavor develops rapidly in the first few weeks and only matures slightly after a a few months, because there's not much more flavor to extract after that.
Liquor variety affects flavor perception, but what you should use should depend on your desired end result. 90% of the time I'm trying to highlight the fruit, so a neutral vodka is fine. But I've used tequila for habanero, gin for a lemon-lychee infusion, and I typically like an inexpensive aged rum for things like jujube dates (which I cut and cook in syrup before infusing), because it adds a bit of wood and still has a flavor profile that matches the fruit nicely. My friend told me his mother-in-law made ume-shu in Remy Martin VS cognac, which he said was the best ume-shu he's had, but essentially what you're buying there is some free (as in time) aging in wood, which adds some nice flavor notes.