Treat thawed worms the same way you would treat raw meat that you just took out of the freezer to thaw. The same general rules apply--do not leave it out any longer than necessary, and do not re-freeze once you've thawed it out.
Personally, I don't want to risk feeding my fish contaminated food, and outside the freezer small amounts of food can be compromised by bacteria fairly quickly. I never store it in the refrigerator or leave it out before feeding. I just take a cube, cut off what I need with a paring knife, and put the cube in a ziplock bag and put it back in the freezer before it melts. Then I throw the piece of cube in a cup of tank water, which is usually about 80 degrees, so the cube thaws instantly. Then I use a pipette to feed each fish.
If there is any left over, I either put it in my community tank, or throw it away. I would rather spend an extra minute on food prep and waste a few worms than risk contaminating all my stock--maybe a little overkill, but to me this way just makes sense.