Hot Pixels

I've noticed more and more that I have some so called hot pixels on my camera's sensor. I decided to test it out a bit so I took a series of photos (1 second, 2 seconds, 5 seconds, 10 seconds, 25 seconds and 45 seconds exposures) in complete darkness with the lens cap on. Then I looked at the photos in 100% on my computer and in the 1 second exposure I couldn't find a single pixel that wasn't black. That's good. In the 2 seconds exposure I was able to find one dark gray pixel. That exact pixel just got brighter and brighter the longer the exposure got. It even got some friends to join in around it.

Here's that pixel in 400% zoom in the different exposures.
From left to right it's 2 seconds, 5 seconds, 10 seconds, 25 seconds and 45 seconds.

Then I decided to check for all the hot pixels I could see in 100% zoom of the 45 seconds exposure. I've resized them (400% zoom), cut them out and pasted them in the area they appear in the photos. So they aren't that big in reality, it was more to show where they are and what they look like.

The last photo is to show how well they show up in real photos and not just complete darkness ones. This is the top left hot pixels and the lower right ones in 100% zoom from a not so good 60 seconds exposure of stars. An attempt at making a star trail photo around Polaris.

I'm not sure if it's possible to fix the hot pixel problem, but as long as I don't get longer exposures than 1 second I will be fine. Too bad half my photos are made at night.