Thanks for your question.
You are quite correct. God does not tempt us to sin. However, He does lead us into trial. The word "temptation," unfortunately, is ambiguous because it can mean either "trial" or "test of faith" as well as tempation to sin. James tells us in James 1:13-15 Let no man say when he is tempted, I am tempted of God: for God cannot be tempted with evil, neither tempteth he any man: But every man is tempted, when he is drawn away of his own lust, and enticed. Then when lust hath conceived, it bringeth forth sin: and sin, when it is finished, bringeth forth death.
Even the Lord Jesus, in the Garden of Gethsemane, prayed to avoid the trial of the cross. But notice that he added the qualifying statement "Thy will be done." No one wants to undergo unpleasant circumstances in life. In this, the Bible is very sane and realistic. There is no seeking for martyrdom in the Bible! However, although we pray to avoid such hardships, often the answer, as it was with the Lord in the garden, is "No." Paul, in Romans 8:28, tells us that "all things work together for good" in our lives - even the tragedies and hardships. Sometimes we need the trial of faith to learn hard lessons and to prepare ourselves for eternal life in God's Kingdom. See Hebrews 12:1-13.
In the Bible, tempation can mean either a trial or an enticement to sin. The same with the word "evil" - it can mean either thoughts and actions and events which are sinful or it can mean a difficult event or disaster. So, in this sense hurricane Katrina was evil but not sinful. It was a trial but not a temptation. However, the first chapter of the epistle of James is focused on warning those who were enduring terrible trial by persecution not to fall into temptation to sin because of it. Some of the Christians in James' day were actually blaming God for their lack of strenth in dealing with trial, then giving up and falling back into a life of sinfulness and then saying, "Well it's God's fault that I have fallen into sin because He brought these problems into my life." Trial is brought into our lives to strengthen us but we have the choice of overcoming by God's grace and power or succumbing to circumstance and falling into sin.
See 1 Corinthians 10:13 [note here is a perfect example of the word "temptation" meaning "trial."]
I hope this has been helpful,