Yes! Coffee does help burn fats. What it does is it increases the rates of metabolism thus enabling the food one eats to be quickly broken down for energy production.
Nothing more or less can't be taken care of by coffee when comes to burning of fats. I will recommend you try out other viable alternatives too if really you want to burn fats. Endeavour to engage yourself in outdoor activities regularly, like jogging, brisk walking, going on a long distanc trekking, advisable with your pet if you have any: it will motivate you to do this.
Another regime that will help you to burn fat is getting yourself a hot mug cup of ginger and garlic tea laced with lemon after emptying your bowel in the morning. Get raw ginger and garlic, peel their back off them and cut them to smaller bits and pour them into kettle. Pour mugful of water into the kettle and add little more water to it. Allow it to boil for up 3-5 minutes and pour it back into the mug cup. Squeeze half lemon into the boiled water and sip before it's lukewarm. Do this routinely along side your work out exercise, you will be shocked how effective this would be in helping you to burn fats.