I'm glad you didn't say starting pistol... However that would also act as a bird scarrer, thus two birds with one.. Never mind..
Apart from the thermal stress alluded to earlier, is there any other problems associated with only using 1 or 2 engines for the taxi run, bearing in mind the almost 30 minute changeover some of the airlines are now managing...
Would the engine have chance to cool down that far before being restarted anyway?