A Morning Dove Laid An Egg On My Air Conditioner: What Do I Do?

I found this in my inbox yesterday. The subject line read: Eggs and Air Conditioner. I was intrigued. It's from the NYC Bird Club list serve sort of a Park Slope Parents of local bird lovers. To read more or to respond go here: http://forums.manhattanbirdclub.com/post?id=3548966

Yesterday a morning dove laid an egg on top of a towel that I rest on my air conditioner

The towel is very small and only keeps the drops of other air conditioners from making a loud noise on mine.
I called the bird volunteers and at the time there didn't appear to be
a mate and there was no nest so they told me she would most likely not
succeed w/ this first egg.

Lo and behold, after a while, a mate appeared and he began to build a nice nest.

HERE'S MY QUESTION.  If I turn on my air conditioner will I hurt the
baby egg?  I have been surviving with the fan but my apt is HOT and I
can just go buy another AC for another window in another room.

Please send me your thoughts about using the air conditioner.