Thyroid problems or not, an hour at the gym will NOT burn any fat if you are working to the wrong heart rate.
Forget calories burnt on those ghastly machines, and what most ill-informed, often promiscuous, gym instructors tell you. You must work to your FAT BURNING ZONE heart rate.
A lot of overweight people actually work to hard to lose weight via exercise. The heart rate formula has been proven by most proper doctors, and is certainly not "faddy" with mant of these "carb days" "protein days" "eat grapefruit" cr4p I keep hearing about.
There are a few heart rates that are important. To work out your FAT BURNING ZONE use these simple sums:
220 beats per minute (bpm) minus your age is your MAXIMUM heart rate. DO NOT even go close to this UNLESS you are super fit with a good heart.
Lets assume you are 30 years old. 220-30 =190. Therefore 190 is your MAX
For muscle building known as ANAEROBIC (without oxygen) used for explosive sport, ie sprinting heavy weights etc work from 70-90 percent of 190 bpm
For FAT BURNING (aerobic) i.e with oxygen work 60 to 70 percent of your 190bpm.
For a cardio workout (you will NOT burn fat, no matter how many calories burnt, 40-60 percent of your 190bpm
For resting heart rate (healthy) 40 percent or lower of 190bpm
So if you are 30 years old 60-70 percent to optimise FAT BURNING, work aerobically to 114-133 bpm.
Whether this figure is higher or lower depending on your exact age, it is not a strenuous workout.
Invest in a heart monitor or rent one from the gym. The best bit of kit you can have.