Most electric fans, including virtually all factory electric fans are wired to a constant BAT+ source, rather than the ignition switch. The point is to cool it when it needs to be cooled, not just when you're in it. If when you stop and shut off the engine, the fan stays on for more than 5 minutes, either the sensor needs to be adjusted, or there is another problem in your cooling system. 90% of the time, the fan should have cooled enough to shut off before you go to restart. This means that there won't be another item competing with the starter.
If you are hell bent on powering it from the ignition, and you want the fan to pause while starting, the answer is simple. Use a relay, and have the trigger wire attached to an accessory fuse source. Accessory fuses and power sources are cut off when the ignition switch is turned to the start position, and then powered when the key is either in the run or Acc position. This is why the radio, the lights, and every other accessory shuts off when you turn the key to the start position, but comes back on when you release the key.
Take care,
-Chris
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