I have two of those Marina Betta heaters, and I like them a lot! They're both in 3 gal tanks, and they work very well. The water stays a consistent 79F, which is considered 'perfect' for Bettas. There's also a tiny red light on it, so you can see that it's on.
I don't know how it would be in a one gallon tank, but I'd say go ahead and try it. I think it'll be fine! (And if it's not, Petsmart has a good return policy.)
Also, get the floating glass thermometer. It's $2.99 at Petsmart, and it's more reliable than one of those stick-on ones. Here's a link: Petsmart Floating Glass Thermometer