It's not regularly as hot where I am as in Iowa, but my commute is a little longer than yours and it can be quite warm during a heat wave. I carry my lunch almost every day.

I have an insulated lunch box I throw in a pannier. Keeping everything in the fridge before transporting it makes a difference as does blue ice. If you add an apple to your lunch that has been stored in the fridge, it will help your lunch cold.

If you have a fridge at work, you can put stuff there when you arrive. The lunch I eat most often is a turkey sandwich with cheese smothered in mayo. I don't bother to refrigerate my lunch at all or add blue ice and it is always warm when I eat it. As I say this, I think my wife might throw blue ice in my box sometimes when it is especially hot (which would probably be just normal weather for you).

A couple observations. Cheese will not spoil that fast. You can leave it out just fine when it's hot and eat it. I have literally left cheese out for days with no problems. If you don't eat real mayo, that probably won't spoil either since it is likely to be made of oil. Even if you do eat real mayo, stuff just doesn't go bad nearly as fast as people say. I've let stuff sit out all day, throw it in the fridge, and eat it the next day. It never causes problems.

Don't mess with the microwave stuff. For a 28 mile commute, you need to eat something with more substance. Besides, packing your own lunch is much cheaper and tastes better.