No. There's no way to safely heat or cycle it.
Anyways, they're too small to have any fun decorating and customizing!
@ Devon, you are incorrect.
"In the case of Bettas, these amazing fish come from a Tropical Habitat "
Exactly. Bettas come from tropical regions. You know what that means? They need a heater. And do you know what often happens to heaters in tanks less than 3 gallons? They parboil the fish. You know what else? They have a significantly high chance of catching on FIRE, and even EXPLODING if the water level evaporates too low, which in a bowl, can happen in a few hours. Without a heater the fish cannot metabolize correctly. Bowl and heaters less than 15W are dangerous. They are not adjustable, and not submersible either which leads to damaging the heating element. Bettas need their water at a constant 78F. External sources will not do that, and will fluctuate greatly.Tell me, did any of your fish live at least 7 years of age?
Furthermore, the tropics are actually very stable. Fish in tropical regions cannot be aged by otoliths, because there are no temperature variations to cause growth rings. Also, bettas come from swamps and rice paddies, which while shallow, hold thousands of gallons. Water holds heat for a long time, and in thousands of gallons the change will be incredibly slow, only a few degrees difference. In a bowl, the constant swings from drafts will stress the fish and kill it. Even dry season puddles have thousands of gallons of groundwater feeding them. Bettas and many other fish that live in areas with a dry season do often die in the puddles, with survivors having moved to permanent water sources as the water had begun to recede.
"Nutrients depletes quickly in small spaces"
Wrong again. Nutrients BUILDS UP too quickly in small spaces, which rots and forms toxic ammonia. In a small space, the ammonia will build up quickly, and ammonia damage is cumulative by week, So even with regular cleanings, it will eventually succumb before its time. Constant cleaning will also stress the fish, and stress is cumulative for long term. The fact that you think "nutrients" is the substance and that it depletes shows how little knowledge you actually possess on betta care.
Where on earth did these "articles" come from? A 5 year old?
Seriously, do some more research. Aquariums are a science and a balance. The animal's habitat is supposed to be ideal for it.
*It's not that they're impossible to control, temperature is close to it. In the smaller body of water, there is less stability. For example if you put two containers of water in the freezer, the smaller container will freeze first because it won't take as long to chill. The temperature in a 1 gallon bowl is going to swing faster and more readily than in a 10 gallon aquarium. Sure it can be cycled, I misspoke there too, but not effectively enough for a vertebrate inhabitant. Again, it's a simple dilution. Put a drop of ammonia in a 1 gallon bowl, and the ppm will be higher than that same drop in a 10 gallon aquarium.
Keeping a bowl IS more difficult. It requires more frequent water changes to dilute that very ammonia that would have spread more thinly in a larger aquarium. The smaller volume means the temperature will swing more drastically should a draft hit it than in a larger aquarium. And heaters ARE inherently dangerous in ANY aquarium, just more so in smaller ones.
And not to forget this person seems like a beginner. What might work for you might not be under their capability belt yet.
Devon, we're trying to help this person start the hobby on a good note, not a dead fish in a bowl. You're taking this way too seriously. So what, you choose to keep a betta in a bowl. That's done. There's no changing your mind. These responses are not for you to change your mind, they're directing the the OP to success. Trying to steer them in the right direction. Again, they seem like a beginner, and a bowl would ruin the experience for a beginner. While a confined space, and lack of heat and filtration is considered cruel and fish bowls are actually banned in some parts of the world. You don't need to go and tell everyone that it's cruel. It's the Internet and people you may never meet. Brush it off, take something away from it, and go on with your life.
As for the articles, your articles come from a website aimed towards selling products to people, and a blog, and both are ".com" domains. Not the best sources. ".com" sources aren't too reliable for research either.
A small volume is very difficult for most people to care for, and this person is based in Canada, so ambient air temperatures are probably lower than where you are too.