How do I change the image of my podcast?

Create a new image with a different name. Change the 'itunes:image' tag to reflect this. Upload both to the server. It won't change immediately: you might be able to hasten it by pinging iTunes, see:

http://www.apple.com/itunes/whatson/podcasts/specs.html#episodes

That's what you do when you handle the feed file yourself. As you are with FeedBurner you will have to check on how to do effectively the same thing using them.

iTunes doesn't come into it. A podcast is accompanied by an xml file (a text file in a particular format) which carried the information the iTunes Store needs to display your podcast and the associated image. This page explains the process:

http://homepage.mac.com/rfwilmut/notes/podcast.html

However if you created the podcast using Feedburner you will need to make the changes there, following their instructions. They presumably have a place where you specify the podcast image, so you need to create a new image with a different name and tell Feedburner the change.