5D2 - hot/stuck pixel even on short exposures

I've just bought a new 5D2, ans the first thing I did was take a (tethered) shot to see how clean the sensor was. The shot was about 0.8 sec and one of the first things I noticed was a pink hot pixel on the left side of the lower third of the image. I tried 30 sec and 60 exposures with the lens cap on, which really emphasised it. There were maybe three other hot pixels for these exposure lengths. I then took some shots using faster exposures. The hot pixel was still pretty obvious even at 0.1 sec.

Is this something to be concerned about? I mainly shoot landscapes, so longer exposures are pretty normal for me. I always do a little editing of course, but I'm concerned this is going to be a real issue.

Any advice or comments would be gratefully received.

I think you can map them out :
"Here is the remap the sensor process:

1. Remove lens

2. Install camera body cap and power-up camera

3. Make sure a full charged battery is installed

4. Place the camera in manual sensor clean mode for five minutes. Make sure the camera body cap remains in place for the full five minutes.

5. Turn camera power off

6. Reinstall lens and test"

TBH I'd be very disappointed after spending at least £3K. Try the above and decide from there.

Foggiest, I owe you one!

The above method appears to have totally sorted the issue. I have just a few very faint blue spots now on a 30 second exposure, and no sign at all of the pink one which was giving me palpitations!

Thanks again.