How to keep a lunch box fresh for more than 2 hours?

For a great answer on safety and temperature, see this answer.

For your lunch, you could get an reusable ice pack to keep your food chilled.

You could also separate the ingredients that need to stay chilled from those that don't and mix them just prior to eating.

There are a lot of salads that will store well in an insulated bag and an ice-pack. If you store the dressing separately, you'll keep everything dry and more likely to be fresh when you eat in 3-5 hours, too.

As someone else mentioned, you can easily pick up an insulated bag from Walmart, or other retailers.

You can store protein for your salad, like chicken or turkey, or tofu, in a separate container, or together without dressing, as long as it's with an icepack. The ice pack can allow you to store the foods for a full day, or until the ice completely melts.

You can freeze the contents of your lunch box prior to commuting, so that it will stay cold longer. Of course it'll depend on what kind of food you've prepared, as some kinds of food are more amenable to freezing than others.

In the tropics. When I go to the market or need food kept cold. I bring insulated bags. About the size on W Mart bags in America. With velcro seal tops. I put in 1 bottle of ice from freezer. Before leaving home. By time to market cold inside. Good for other food also. Keeps food cool even in a hot car. They sweat on the outside. So double cooler. As outside will be cool inside cold. bottle of ice size can very as to how long to keep cold.+ you have some ice water with you. Can be folded over if bag with lunch set on shelf for extra cool. Look like Holden bags I looked up on internet. But I buy Uni Top bags. Store name in Philippines. Great for beach, car trips, shopping, or lunch bag. Use plastic soda bottles to freeze my ice in for them. Have sponge insulation as middle layer. slick nylon liner inside heavy nylon outside for wear.