If you have QDS logging on, yes it will create a tasklog for each publisher task that executes. Go to QMC>system>setup>Distribution services>qds@<servername> > general > under settings for QDS.
You have two options:
1- You can turn off the logging by selecting "No logging" and hit apply --> will stop all logging
2- Change the application data folder - If you have another disk attached that is bigger that "C:" you can move the application folder and you can avoid the C drive to fill up.