If I remember right, historically speaking, interim coaches that then become the HC the following year do not pan out well for the team.
Not saying that Brown cannot be a good to great HC someday, but history suggests it will not be for the Bears either way.
This is the list since 2000:
Dick LaBeau: 4-9, 6-10, 2-14: Win percentage: 26.7%
Dave McGinnis: 1-8, 7-9, 5-11, 4-12: Win percentage: 29.8%
Mike Tice: 0-1, 6-10, 9-7, 8-8, 9-7: Win percentage: 49.8% (made the playoffs once and went 1-1)
Tom Cable: 4-8, 5-11, 8-8: Win percentage: 38.6%
Mike Singletary: 5-4, 8-8, 5-10: Win percentage: 45%
Jason Garrett: 85-67 overall record: Win percentage: 55.9% (Made the playoffs 3 times in 10 years and went 2-3)
Leslie Frazier: 3-3, 3-13, 10-6, 5-10-1: Win percentage: 39.8% (made the playoffs once and went 0-1)
Jim Tomsula: 1-0, 5-11 Win percentage: 35.3%
Romeo Crennel: 2-1, 2-14: Win percentage: 21.1%
Mike Mularkey: 2-7, 9-7, 9-7: Win Percentage: 48.8% (made the playoffs once and went 1-1)
Dough Marrone: 23-43 total record: Win Percentage: 24.8% (made the playoffs once and went 2-1)
Antonio Pierce: 5-4, 2-9: Win Percentage: 35%
5 of the 12 had went to the playoffs at least once, but only one had a win percentage of above 50 during their time with that team. Mike Tice would have been at 50% if you don't count his 0-1 interim record, and Mularkey would have also been above .500 if you don't count his interim record.
Either way.. not an impressive list.