Here it, for what it's worth.
Right-leaning thinkers from Edmund Burke to Friedrich Hayek understood that emotion is prone to overshadow reason. They understood that emotion can be a wise guide in some circumstances and a dangerous deceiver in others. It’s not whether judges rely on emotion and empathy, it’s how they educate their sentiments within the discipline of manners and morals, tradition and practice.Uh huh.
Once again we find ourselves presented with a classic Conservative trick. Emotion and empathy aren't the same thing. Arguing against empathy per se is harder to do, though, so Brook assumes that empathic judgement leads to emotional judgement, and then says that's bad. 
Without access to the whole piece, I obviously have to be careful in drawing conclusions. What I feel comfortable saying is that Brook will, almost certainly, be trying one of two things. Either he will be hoping no-one notices his rather shoddy sleight of hand (which is both dishonest and insulting to his readers), or he earlier (or later) in the column will have conceded that "No-one is saying empathic judgements are or must lead to emotional judgments, but" which is a fairly common tactic amongst journalists and commentators and essentially means "I can't object to the current situation A, so I'll object to B, a situation that hasn't occurred, and then point out that B is not unreachable from A". Which is more honest, of course, but also renders the whole thing kind of pointless.
My main problem with this paragraph, though, is the suggestion that it's right-leaning thinkers who are aware that emotion can cloud reason. It isn't. Smart people across the board that are aware of that, thank you very much. Anyone who thinks that the right has clear-headed thinking sewn up really hasn't been paying attention.
Update: Thanks to Tom, I've finally read the entire text of Brook's column. It's actually very strong in a lot of places, but I stand by my original conclusion that he's conflated empathy and emotion and gone on from there.
 Which is often true, but it's worth noting that a combination of emotional and empathic judging would be superior to emotional judging on its own, since the former means letting ones sympathy get in the way, and the latter substitutes that sympathy for naked self-interest. It's also fun to listen to a man who supported John McCain (who ran a campaign that, whatever else it was, was pretty unambiguously aimed at persuading people to vote emotionally) suggest that cool-headed logic is a good thing. Or maybe I'm being unfair. Brooks notes the right understands how emotion can lead to bad decisions, but he doesn't actually suggest it's wrong to manipulate that truth to one's own ends.