If you have a basking lamp then you don't need a heat mat
As long as the floor gets up to the right temperature then it's fine... ambient temps aren't as important as floor temps.
There can be a chance of competition in both genders unfortunately... if they feel the need to dominate one another for food, space, hides, etc. then there could be problems. This isn't always the case but just be aware it could happen at any time, so you'll always have to keep a close eye on them both for signs of dominance. With a 4ft vivarium the chances are lessened as they have more space to escape each other, but it doesn't kill the possibility of competition entirely
With regards the UV and determining day/night cycles, as long as they are in a well-lit room then they can determine the day/night times fine
2 of my 4 geckos (different species but the concept is the same) have no light source other than the daylight through my bedroom window to tell them when it's day or night
If you'd like to introduce a light source then that's fine as long as they don't compromise the existing temperatures.