Yeast Temperature Sensitivity

I brewed a GumballHead Clone on Saturday. I put the primary in a big basin about half full of water and draped a towel over it with a fan pointed at it. I have been feeding the basin bottles of ice to keep things cool. I have had a heck of a time maintaining a steady temperature. It varies from 60 to 70 degrees. Will the constant variation in temperature hurt the yeast or does it only care that it doesn't get too hot?

Is the 60-70 degrees the temperature of the water that your primary is sitting in? or the temp in side the fermentor? If you've maintained the 60-70 in the water basin then you're probably holding a steady temp inside the primary. Don't worry.

It is the temperature of the bath. Thanks for the response. I was nervous. Been checking the temp every hour all day!!!