is antioxidants damaged by heat?!

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Yes they is.

Cooking actually boosts the antioxidant properties of tomatoes. See link.

From the link: "This research demonstrates that heat processing actually enhanced the nutritional value of tomatoes by increasing the lycopene content -- a phytochemical that makes tomatoes red -- that can be absorbed by the body, as well as the total antioxidant activity. The research dispels the popular notion that processed fruits and vegetables have lower nutritional value than fresh produce."--

You gotta be careful on the internet. There are lots of people willing to give advice who don't know much. Learn to use Google.

ADDED: From the second link: "Peanuts contain high concentrations of antioxidant polyphenols, roasting boosts its overall antioxidant content by as much as 22 per cent. Roasted peanuts are far richer in antioxidants than apples, beets and carrots and comparable to the antioxidant content of strawberries and blackberries."--

http://www.sciencedaily.com/releases/200…

http://www.fatfreekitchen.com/nutrition/…

Many fruits are pasteurized but still contain about the same amount of antioxidants.

Pasteurizing the fruit is for safety reasons, to keep bacteria from growing. So this has to be considered a health benefit too!
However, I did find some studies that seem to answer your question. One, Biodiversity of Total Phenolics, Antioxidant Capacity, and Juice Quality in Apple Cider Taxa that was submitted to the Journal of Horticulture, Environment and Biotechnology examined the effect pasteurization has on phenols and antioxidants. They found no effect on the phenol content of apple juice after pasteurization, but in fact there was a "significant effect" on the antioxidant activity.

Another study found a significant reduction in carotenoids (namely violaxanthin and lutein) after the pasteurization of Valencia orange juice (Effect of thermal pasteurization and concentration on carotenoid composition of Brazilian Valencia orange juice from Food Chemistry in 2004).

So, it turns out that pasteurization does have an effect on some of the components that are healthy in juices: however, it does outweigh the risk of getting sick from bacteria that can grow in juices that aren't pasteurized.
The bottom line is that it's probably best to eat the fruit when you can, and drink a safer (pasteurized) juice that gives you a bit fewer of the antioxidants and vitamins when the fresh fruit is not available.

There are many 'antioxidants.' Omega-3 fatty acids are damaged by heat and light. Citric Acid (vitamin c) will break down at high temperatures, i.e. 175 degrees.