I can speak for my Galaxy S3. I recorded a few short dashcam videos, including a 20 minute night video and it got really warm. Warm to the point of continued/daily use causing damage, especially on hot sunny days. I would consider a cell phone not a great choice for a dash cam
S4 here. I used Daily Roads and my phone got so hot, the camera broke. Luckily, it fixed itself, but I really wouldn't recommend it as a dashcam. The note 3 is too big and might run too hot.