Contrary to what the pet stores would have you believe, every single betta fish needs more care than a small bowl. They make you think you're really upping their lifestyle by moving them from a small cup to a small bowl. The reason they can survive like this is because they can gulp air. Of course, they can also use their gills like all fish, but in the water's oxygen content becomes very low, they can gulp air from the surface. You'll notice I said survive and not live/thrive.
I'm definitely not trying to come down on you. This is considered the norm and is perpetuated by the pet store industry. Here is something to think about, though. Like any animal, the betta fish is going to have an ideal habitat. They are going to prefer oxygenated water, low pollution in their water, appropriate kinds and amounts of food, and an area they can claim as their territory.
Let's start with the pollution, which is the main problem that's run into with bettas. Ideally, fish would live in an ecosystem that maintained itself. Fish would eat and produce waste. The waste raises the nitrate (nitrite? I forget) levels in the water. Plants process it and make the water cleaner. It's a cycle. In the home aquarium, you actually can make a self sustaining setup, minus adding some water for evaporation, but most people don't do this. Most people use a filter and artificial plants. How that works is that the filter pad takes out the physically large particles. It also provides a surface for good algae to grow on. These help brake down the nitrates, and while you should remove excess algae, you shouldn't scrub it perfectly clean and sanitize it. The carbon in the filter helps to remove toxins that the algae didn't. When you replace a filter pad, you're really just replacing the carbon. Then the water is returned to the tank. Since it was agitated and dropped back in, it also helps aerate the water. Besides the algae there are other bacteria and microbes in a healthy tank that help break down fish waste and toxins. That's why you can't set up a tank and dump fish in the same day. Most people recommend letting the tank cycle for a minimum of a week and that's if you dump in some water from a running aquarium to kick start the bacterial growth.
The more water there is per fish, the more buffer you have. If you have a well balanced tank, you can add more fish. If you add too many, you start to raise the toxin levels and the fish get sick. You then either have to reduce the fish, add more plants, or treat the water in some other way.
One thing that helps is water changes. For most people this is changing no more than 20% of the water in the tank and for those without live plants, often coincides with vacuuming the gravel. The change helps remove the excess toxins and waste, but you're also loosing some of the good bacteria as well. They have to replenish themselves. The problem with a small betta bowl is that a 20% water change on a bowl that small is a really big shock. Also, if you're on any kind of chlorinated water, even treated, it's another big shock to the fish. Again, it's about the buffer. 20% of a 30gal tank is only 6gal. That leaves 24gal of stable water the fish is used to. It's a much greater change when you're changing 20% of a couple of cups of liquid.
So basically, when they're in these small bowls, they're living in low oxygen water, sitting in their own waste, and dealing with toxic levels of bad stuff. Even when they get a water change to reduce the bad stuff, it doesn't leave them with enough of the good stuff.
Also, this fish comes from a warmer part of the world and enjoys more heat. Even if they are okay with the cold, again, it's about that buffer. It takes a lot more to cool or heat a big tank that a small bowl of water. That means the temp can fluctuate quickly and that wills stress your fish as well.
So how to do we fix this. The easiest and cheapest thing I would do is go out a purchase a small tank with a built in filter and light, then add a tank heater that allows you to set the temp. Here is an example:
I had a small tank like this in college, and it worked great. I took a listless betta and added him to this tank and you wouldn't believe the difference. He went form sitting on the bottom of the cup almost leaning over to swimming strongly around the tank and playing in the water return.
I'm not saying that there isn't something wrong with your fish, either old age or disease. However, from what you've said, it sounds like it or any future fish would greatly benefit from this upgrade. Additionally, while bettas are territorial with other male bettas, they are fine with other fish. You can get a couple of extra fish to add in with him. Just be careful that you get docile fish as even guppies can nip his pretty tail. I've even had a betta in a 35gal and they've done great with all the other fish. He spent a lot of time cruising around the tank and playing in the water return. Give it a try and I really think you'll see a difference in your fish. Good luck.