There is no 'Thibaudeau style of training"...my "style" is solving problems... heck I train bodybuilder and crossfit athletes... not exactly the same type of training!
I have trained some athletes who compete in firefit. One of my client is actually a 65 years sold firefighter who still compete and could beat many guys 1/3 his age!
NOW my firefit competitors are also Crossfit athletes. So the training we use is similar to crossfit training but with less high skill movements like muscle ups and the full Olympic lifts and more emphasis on loaded carries.
Every workout starts with a strength lift with the purpose of getting as strong as possible... the stronger you are, the easier the carries will be.
We have 2 deadlift workouts per week, 1 squat workout and 2 upper body sessions (normally 1 push and 1 pull).
Then we have carries for strength. Going short distances but very heavy using various types of carries (Zercher, overhead, farmer's walk, prowler pushing, sled pull, 1 hand farmer's walk). We only have 1 type of carry per session and do 6-10 sets of 20-30m with as heavy as possible. I often add rope climbs at the end of the carries too.
Then we have a metcon session consisting of a fatigue circuit which combines carries for distance and speed, bodyweight metcon drills (burpees, box jumps, stair sprints) and weighted metcon drills (thrusters, KB swings, sledgehammer striking etc.) as well as metcon specific drills like the assault bike and rower.
I design circuits that last about 3-5 minutes to complete and we perform it 3-5 times.