Just walking won't do that much because it won't raise your heart rate high enough to start burning what you already have. It's good for maintaining yourself once you reach your target weight/size, but not so great for losing it.
As you've already noted, exercising in the heat isn't a crash hot idea when starting out, but doing at least some exercise every day is.
Any diet that says "just eat/drink this one thing 'cos it has vitamins/deoxidizers/pixie dust" you can safely ignore because as Svengali said - BALANCE is important. The old Food Pyramid that we so easily forget. Lots of fresh fruit and vegetables, some breads and meats and only a little sugar.
Of course, specific people have special requirements - so listen to your doctor if they tell you something (such as eating less salt).
Specific ideas to help:
- Eat more often, in smaller quantities. By having six small meals rather than three normal ones (or worse, one or two big ones) then your metabolism will speed up and you'll burn weight faster.
- Move faster, lift less. You want to focus more on "make you sweat" exercise rather than "build muscle" exercises.
- Muscle is heavier than Fat. Remember that when you are first starting, you'll gain a bit of weight as you are losing weight. You're burning off fat, but gaining muscle. So pay more attention to the measuring tape rather than the scales.
- Be consistent. If you do lots of hardcore exercise on Monday, nothing on Tuesday and Wednesday then a bit on Thursday and nothing until the following Monday then you won't lose any weight. There's a reason brickies labourers are more buff than office drones - they spend all day lifting heavy things.
- Water. Lots of water. Not only good for hydration, it'll help keep your kidneys clean and healthy. Fruit juice is good, but has a lot of sugar. Sports drinks are good but have lots of chemicals. Milk is bad, unless you're trying to gain weight. Again - balance. Have some milk in your tea or coffee, but don't have a milkshake with lunch. Sports drinks are good, but not every day.
Incidentally, you can make some pretty good home-brew "sports" drink by grabbing a bottle of water and adding half a lemon worth of lemon juice, a teaspoon of sugar and a teensy bit of salt. (Optionally, you can add a small amount of cordial and omit the sugar for better flavour).
Final advice: write it down! An unwritten goal is a wish. So write down what you want to do, record what you have done, keep track of your statistics (weight, waist, upper arms, upper thighs, etc) so you can track the changes and you'll start to notice the difference.
The final ingredient - time. It'll probably take the better part of a year to get yourself healthy, so don't expect massive changes each week. Unless you have two personal trainers and a tv crew following you around all day, odds are that it'll take you a bit of time to start seeing some changes. But as long as you are trying, you'll be getting healthier.