It is generally accepted within the scientific community that there have been numerous times in our Earth's past in which there was little or no ice on Earth at all. During much of the time of the dinosaurs (65-230 million years ago), most of the world had tropical weather and carbon concentration in the atmosphere may have been several times higher than today.
A bit more controversial but gaining popularity among climate scientists is the idea that at several times in the past, our world may have been entirely frozen except, perhaps, for a belt of slushy ocean near the equator.
Geology provides the evidence for both scenarios in the forms of fossilized tropical plants and rocks that had to have been formed underneath glaciers. These "natural" climate changes in the past have had numerous causes including changes in volcanic activity, changes in ocean currents from continental drift, and various effects from evolving and expanding life forms. Apparently, we humans are not the first life forms to have affected the atmosphere's carbon concentration.