too much circulating T3 can cause sypmptoms of hyperthyroidism... which are not pleasant. There are certainly very effective weight loss supplements out there which are safer.
Sounds like your trainer is more interested in clients getting 'fast' results (making him look good) then doing it the right way.. if your new to training and have a bit of fat to lose, it's not to hard to drop 2-4 pounds a week given a good diet and appropriate training, without any supplements. Your trainer should have focused on your dietary habits and a solid training regime before throwing potentially dangerous and unneccessary supplements at you.
My reccomendation: Get a new trainer. Focus on diet and training. Eat 20-30% below maintenance, high protein, moderate to low carbs, moderate fats. train hard. Add some creatine, multivitamin, fish oils, then possibly some fat loss supps (many choices, do some searching). Don't fat you spent years putting on to be gone in 4 weeks. Give yourself 2-4 months to lose the 20 pounds properly, meaning mainting lean body mass at the same time, and you'll look and feel better. Rely on T3 to increase metabolic output and tissue degeneration and sure you'll lose fat and muscle, but at the end you'll stop taking it, your body will have an even lower metabolic rate due to decreased lean muscle mass, and you'll have learnt little in the diet/training discipline, probably go back to old habits and put on more weight than you lost as this time you have even less muscle then when you started.
My 2 cents, good luck.
nate