Our subject matter is Heaven, God, and man's salvation. Dante's views on these things are very clear. He wants them; he loves them; he wants to know everything about them.
So let's start with "passionate," shall we? Passion runs two ways. Author-Dante gets so excited about Beatrice's beauty that he becomes speechless, but he also vents against corrupt clerics and showy preachers. It is obvious from the way author-Dante characterizes Beatrice, St. Thomas, Cacciaguida, Mary, and God himself that he adores them all. They are all "beautiful," "radiant," or "joyous." Over the starry Cross and Eagle and Celestial Rose, Dante works himself into a literary frenzy, waxing poetic on the object of desire for pages on end. But just as quickly and just as enthusiastically, Dante can become the Dante we know from the second half of Inferno – condemnatory and righteously enraged. The way in which he sees the Earth, as "scrawny" and as "a little threshing floor," shows to us his deep disdain for all things petty.
On the other hand, Dante's curiosity about theological matters is voracious. That author-Dante includes the views of past scholars, even those with whom he disagrees (like St. Gregory in Canto XXVIII) shows that he has done his homework and wants to resolve controversial theological issues – like what correct angelology is and how many angels there are. Despite all the rhetoric about faith, Dante does everything he can to make sure we readers understand his explanation. He makes it very cerebral and logical so that our brains can follow. Thus, author-Dante does much to make clear his passionate and curious tone.