I don’t remember the Connecticut chat, lol, but I was probably referring to warming up for speed work and the possible contrast in temperature and muscles’ reaction when moving from in- to out-doors. In case of a tempo session I would add layers of clothes, increase general warm up duration obviously, completely avoid anything static (e.g., stretching, slow drills, etc) and go easy with range of motion. In any case, don’t train hard on such a day, not to ‘exhaustion’. If you think it will help you with this particular issue (i.e., abdomen area), add some easy core work indoors, try it. I would still prefer warming up outdoors altogether, but as John says do what you have to do. Others?
Edit: a tempo session is a tempo session -it helps with the ‘aerobic component and fitness’ as you say, but not for the 400 m per se, as 400 m speed isn’t there; if this is what you are asking.