What ISO are you using? The higher the ISO, the more noise will appear, and in a dark shot, it can show up more than usual. I use my 300D for exposures up to 2 minutes, and I haven't found much issue with the sort of hot-pixels you're reporting.
However, as karmat said, the sensor heating up could be having an effect on it. On long exposures, it does get warm. However, "long" would usually be a bit longer than just a second or two - more like minutes.
See if you can post a shot sometime, so we can all take a look.
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