Betta Fish breeding.?

I bought a male betta fish 2 days ago and its white with like black eyes and the tail and fins are greeny-turquoise.

He's in a REALLY small tank. It's not a tank. It's a like.. bowl/square shaped betta starter kit thing. And I'm too cheap to buy a 5-10 gallon filtered and heated tank. I keep a hot lamp over it because bettas are tropical fish.

I bought a female today. She's not very small a bit smaller than Czar (male betta). I just put her in with him, because the pet store guy told me it would be alright. But i'm reading all this stuff about them killing each other. And people are like "nah, it's fine" and others are like "dont they'll kill eachother" I'm wondering if they will just spawn in that little fish thing without doing the whole introductory procedure thing.

Thankss