Congrats on the new betta! Just FTR, the OP is in Sweden, so some of the advice like check Petco/Amazon etc. doesn't really work for the OP, other than as a reference guide.
None of my bettas are in a bowl, I've always kept mine in at least 2.5 gallons. However, my son recently had some Triops in a one gallon bowl, and I put a Betta Stik in it. It didn't heat the water very well, I had to keep the bowl half empty in order for it to work. You will just need to shop around for a heater. (also, the first two links the above poster provided do not work for me) Of course your home might be warmer than mine, and a Betta Stik or something similar might work for you.
Sticker thermometers have always been pretty accurate for me, I don't think it would be too far off the mark in a bowl, as long as the sticker is placed low enough to cover the area with water.
One thing the OP hasn't stated yet, is what kind of water conditioner they are using. When adding a fish after a water change/new water, instead of just "dropping" it in (and I don't mean literally dropping it, lol---I don't think that's what bettafishlover meant ) you need to add a water conditioner first to remove chlorine. I assume the water is chlorinated in Sweden? I don't know how the water is treated there, public water suppliers usually treat it with chlorine, but that is very harmful to fish. Also, in the future if you purchase a new fish, you should float the fish in it's bag in the bowl/tank for 15-20 minutes so the water temp will match and not be such a shock to your fish. I'm sure that's what bettafishlover was asking, if you had acclimated the betta first, rather than just "dropping" her in.