I appreciate the attempt at science here but space has almost no drag. She could just turn her engines off and still be going the same speed. By continually running the engine she's just continually accelerating. She could totally just turn the engines off and let things cool down which would actually reduce her heat signature unlike building up a whole ship sauna. Bad sci-fi writing loves the idea that you constantly need to be burning fuel to be moving forward when that isn't how it works in a vacuum.