I too have gotten the dry (or not so dry) heaves from cycling.

In fact I got my first taste after picking up my first bike, riding up a hill and had to stop. I was so unfit!

Apart from heat and too high a heart rate I have also found nausea/dry heaves linked to how fit you are and over-extending yourself.

I haven't have the heaves for a few years now and I put it down to drinking from my camelbak constantly, taking breaks and that my fitness level has increased.

Probably not the answer you were looking for as I see you felt you were taking it easy.