Ty Detmer, 1988, 333 vs New Mexico (5 TDs, 0 INTs)
Matt Berry, 2002, 360 vs Wyoming (3 TDs, 2 INTs)
Tanner Mangum, 2015, 309 vs Boise St (2 TDs, 2 INTs)
Tanner Mangum, 2015, 365 vs UConn (2 TDs, 2 INTs)
Tanner Mangum, 2015, 332 vs East Carolina (3 TDs, 0 INTs)
Tanner Mangum, 2015, 336 vs Fresno St (1 TD, 0 INTs)

So it looks like the freshman records he won't have (and may not get) are passing touchdowns and passing attempts in a game.

Detmer had 5 TD passes. Heaps did have four twice.
Heaps had 55 passing attempts vs Utah St. Mangum "only" 53 vs UConn.