This is one of those shady areas of the law. I personally view it as a sketchy deal; what if somebody then wants to buy the item just for the fanart? It is a profit. You are using it as a promotion to bring in people to buy your stuff. Granted a lot of people do that.
I'm having some concerns with my crafts as well and making sure I'm researching my terms- I am very involved with the law and legality concerns personally- I studied it in college. I made my own pillow pet idea for a concept and for sheer fun (I made my own idea with a tie rather then velcro and this and that to make it more me and different) and people now want to buy it- and I refuse to sell anything based off something else without the proper legality claims backing me up seeing the pattern is similar to that of the actual Pillow Pet. So for all those who inquired- I tell them simply it was a concept for fun, for my own enjoyment. I do not intend or plan on selling any because of legality issues- until I either hear back from the company (I contacted Pillow Pets with some questions) or I have full coverage and legal right to do so. So far each individual has respected me for abiding by the law and still continued to place an order for an alternative product because they enjoyed my work. If you are serious about selling fan art you can contact the creator. It might sound crazy but I actually had a friend who asked permission from a gaming company to make up a t shirt with their character and the company respected him so much they asked if he would intern with them for a summer because they liked his work and his morals. They also gave him the permission to sell the design. So it worked wonders for him. It shows you are taking that effort and sometimes it can work out well. Other times not so much.
I steer clear of selling fanart and fan-based works for profit because you never know when somebody will want to make a quick buck off you and sue you. I know people who have had this happen to them and it is not something you want to mess with. For fan art and exchanges I would recommend craft swaps and craft trades over selling. There is no profiting, it is more of a personal task- and nobody is gaining really anything from it other than the joy of their fandom. I see a lot of people going this way to avoid the larger legality concerns of selling.
It's illegal, but you don't see Jessica Nigri getting sued, do you? No one checks individual artists websites. If you get caught, it's because you're waaaay too famous and one of the companies notices.
The problem is distribution, not sales. If you think about file-sharing services, they don't normally charge you for downloads, if they make money it's indirectly, off advertising. So why did copyright holders go after them? Because the right to distribute something belongs to the copyright holder. And fan art is derivative art, and the copyright for derivative art is held by the original copyright holder except in Fair Use cases.
It's not a matter for criminal law, though, so "illegal" isn't really the right term to use. You are violating the copyright holder's rights by distributing fan-art of their work, but it's up to them to take action against you. Will they? Probably not, but you never know. They have the right to.
Technically, as soon as it is not for your own personal use, it is illegal.
And since how the law works is they can sue you for the money they would have made if you had not offered your product, you can still be sued for monetary damages.
On the reality side of it, if they noticed, you would most likely just get a "cease a desist" letter, telling you to stop or they will sue. As long as you listened to that letter, they would not likely persue further legal action.
That would only be the case if you allowed people to receive the item without buying anything. Also, even then, you're using it to promote your business. Which even if you get no direct monatary gain out of it, the fact that you are using it to further your own business goals gives it an abstract value which is also infringing on the intellectual property rights. It would be like if you created a commercial using copyrighted material. The commercial itself gets you no money, it's the effect of the commercial's promotion that gets you money, and you wouldn't be allowed to use copyrighted material in a commercial.