One thing that might help to understand the clergy’s thinking is that most of them (at least further up in the hierarchy) came from noble households, and thus they were reared in that culture of martial accomplishments. Think of Chaucer’s monk in the prologue of the “Canterbury Tales” who wants to spend all of his time hunting and doing noble-like things.
There were voices in the church that argued against violence, but they were definitely in the minority.
“Temporal” is not the same as “secular” in the modern sense; parish priests are “secular clergy” because they are active in society as opposed to the “regular clergy” who are bound by (for example) the Benedictine Rule and live apart in monasteries. Temporal authority is authority exercised in time and on earth (unlike, for example, excommunication) and refers usually to kings and nobles, although some bishops wielded temporal authority in addition to their spiritual authority.