Time of day is personal preference.  As far as utilizing the treadmill to burn fat it's simple and so many different ways. HIIT is one of my favorites, with 15-20 min you will get a sweet workout, brisk walk on inclination as well, even distance once in a while to keep things fresh will help...I personally mix it up as much as I can. 

I prefer to do sprint intervals on the treadmill, it burns fat faster & takes much less time. My created workout is only 8mins long and you do 20 seconds of sprinting as fast as you can without falling off, then 10 second rest where you jump your feet to the sides. Do a few rounds of that and you'll be sweating your ass off and the fat will be melting away