No one ever answered your question but a similar one was asked more recently. Here is what the USGA Handicap Manual states:
a. Temporary Changes
When temporary tees and/or greens are used, the Handicap Committee must notify the authorized golf association. The authorized golf association will decide whether or not scores made under those conditions are to be accepted for handicap purposes, and whether the USGA Course Rating and Slope Rating should be modified temporarily. The Handicap Committee has a responsibility to notify its members that when a hole is not played due to construction, the score for that hole must be par plus any handicap strokes to which the player is entitled. (See Section 4-2.) The procedure for issuing a temporary rating may be found in "The USGA Course Rating System."
95% of the time this is going to leave you and me in a pickle. Most public courses will not go through the effort to notify the state golf association and get a temporary rating. Unless the course provides a temporary rating, my suggestion is to record par plus any handicap strokes as your "official" score for handicap reporting regardless of how you actually play the hole.
So in this instance, if the original hole is a par-5, record a "5" plus any handicap strokes. You may actually have shot a "2" on the now par-3 hole but report 5+ until the hole is restored to a par 5. Essentially, treat it as a "hole not played" and follow the USGA advice of recording par plus any handicap strokes.