Whatever happens in life, there is almost always a solution. So if you have thyroid problems, usually it would be linked to insulin resistance.
So what I would suggest to increase fat loss, is reduce complex carbohydrates such as potatoes, pasta and rice and take food with low GI, i.e. minimum amount of sugars. Your diet needs to consist mostly of veg and lean protein and fruit with minimum amount of sugars. Also, try and minimize diary products as much as possible. Training with weights in circuit training will help fire your metabolism and tone your body.