Of course, searching for accommodation might be different for each city in Germany.
The good thing of smaller cities, in comparison to Stuttgart, Munich, Hamburg, Berlin, Frankfurt, is that the rent cost might be lower.
Heilbronn hasn’t been considered to be Cosmopolite city yet, but I really loved the place.
Curiously, I have lived in Pforzheim and Heilbronn, what some Germans considered them to be ugly cities. In my opinion, Germans have very weird concept of what they consider what is an ugly city. I usually say that I lived in two of the most beautiful cities in Germany.
Of course, you can’t compare a city with 5 million habitants with one with 100 thousand. The number of restaurants, services and activities are way different in amount and types.
Anyways… Regardless of the type of Germany city that you choose, there are website like WG-Gesucht.de where you can find available flats.
The disadvantage that I see, is that many people are looking for flats, and the owner requests you to have a visit. Making it impossible for you if you are in another country.
Universities might have their own accommodation services or at least a list of places to stay. This way it could be easier for international students to find a place to stay in Germany.
I recommend you to search for Facebook Groups, that are realiable, and ask for places to stay. Or give a hunt of posts where people are offering places.
In Heilbronn, there is an internationals groups where you can find people that might be willing to help.
Take into consideration that there will be places that will include services such as Internet, Electricity, Water. This type of rent is called Warmmiete. And there will be places that don’t offer this and you will have to pay it by your own, also known as Kaltmiete.
I recommend you for the first flat, try to find something that is already furnished and with the services included. Why? Because in your first time in Germany, many things might be confusing. So, as you learn to live in Germany, you eventually will get used to the things that you have to do and where to go, plus don’t forget, that you will have to talk German. Therefore at least is better in the beginning to have the flat fournished and don’t worry about that.