Just happened to read something on this in the book When by Daniel Pink. It is a book about circadian rhythms and their effect on performance, not about diet/exercise so not a lot of detail.
Circadian Rhythm
There is an ebb and flow with your body temperature that's the same as night and day.
Circadian Rhythm is the primary factor that determines if are a Night Owl or Early Bird.
Optimal Performance
You preform best when you body temperature is at its highest range and are less efficient when your body temperature is at it lowest.
Thus, training when your body temperature at it highest it optimal.
Plotting Your Circadian Rhythm
1) Take your body temperature when you wake up.
2) Take your body temperature ever two hour after waking.
You will find it fluctuates throughout the day. It will tell you when you are most likely to preform at you best and when your not.
What Your Already Know
Plotting your body temperature will most like reinforce what you already know.
You know what part of day you do well and what part of the day when things drag.
High Octane Training 2 | T Nation
Here is an interesting thing the East German did.
To increase performance via body temperature, the East Germans infected their athletes with a "de-natured viruses to generate a slight fever immediately prior to a world record attempt!"
The downside, as you might expect, was the timing. "Later into the cold, the adverse effects outweigh the benefits..."
He claims that cortisol rises naturally upon waking and that coffee interferes with cortisol production. Therefore he suggest waiting 30-90m after waking up to have our cup-o-joe.
Acute Cortisol
Short term elevation of cortisol occurs after after a night of sleeping and during exercise is a good thing. It along with epinephrine, nor-epinphrine, dopamine and growth hormone burn fat for fuel.
Chronic Cortisol
Long term elevation of cortisol create health issues.
"Coffee interferes with cortisol production."
Pink is a smart guy who does his homework. However, there nothing that I have found that indicate that.
Caffeine/Caffeine and Cortisol
The majority of online information indicates that coffee/caffeine increases cortisol.
Coffee/Caffeine upon waking in a fasted state accelerates body fat being used for fuel.
Caffeine also elevates your body temperature.
"200mg of caffeine can increase blood cortisol levels by 30% in one hour."
https://www.naturallyhard.net/caffeine-cortisol/
Medications
Another interesting caveat is that research shows that when medications are taken at the right time during your Circadian Rhythm it enhances their effect to a greater degree.
Kenny Croxdale
