There's not much Cruz got right here.
First, Cruz conflates the science of climate change with the politics of climate change. Scientists don't scream, "You're a denier". They point to the scientific evidence that human activity is leading to climate warming - the evidence of which is overwhelming. There is no "evidence that disproves their apocalyptical claims", because if there was, scientists would abandon the theory. That's how science works.
Second, science works that way because scientists developed a system in which they created hypotheses and tested them.
So it's silly to say that "accepted scientific wisdom" said the world was flat, because the assumption that the world was flat didn't derive from science. Instead, science challenged the conventional thinking, using a superior system for uncovering the truth.
Third, Galileo came along well after people knew the Earth was round. People had sailed around the world before he was born. His conflict with the church was that he said the Earth revolved around the sun, instead of the opposite. (Actually, his conflict with the church was probably more about his views on transubstantiation, but that's a different topic.) Galileo challenged the orthodoxy based on evidence collected through science.
Fourth, the "warming hiatus" is not "a real problem" for climate scientists, except in the sense that it poses another question to be answered. In fact, scientists have a theory on why temperatures haven't increased as quickly as projected in recent years. (In short: they suspect that it has warmed - but deep in the ocean.) What's more, scientists who studied the satellite data to which Cruz refers reject the idea that it somehow disproves the idea that human activity is making the world warmer.
Fifth. That Newsweek article. Oh man. In 1975, Peter Gwynne wrote a brief for the magazine that suggested that some scientists believed the world was cooling. It was nine paragraphs long, quoting scientists who admitted that their projections were preliminary.
To DailyClimate, Gwynne explained, "It was just an intriguing piece about what a certain group in a certain niche of climatology was thinking."
He added, "Newsweek being Newsweek, we might have pushed the envelope a little bit more than I would have wanted." But that article has fuelled a cottage industry in science rejection.
What Cruz is doing is treating as valid one magazine article from 40 years ago but rejecting as hopelessly flawed study after study showing that the world is warming.
The Galileos on climate change are, like Galileo, the scientists. The people pushing back on the science are, like Cruz, those who favour the status quo. Cruz's comments, from start to finish, are simply not correct.