Flight Instructors Fatigue Reports

"... a FI flies under extremely low temperatures or extremely high temperatures for 4 consecutive hours, VFR, by day or night... " This is rather the exception and not the norm. Rather than creating a regular construct that limits FIs in their jobs, I suggest trusting the required self assessment before every flight: It is mandatory of every pilot to ask yourself whether you are fit to fly. Regardless of any other circumstance.
See also: https://www.easa.europa.eu/community/topics/decision-making-single-pilot . You cannot regulate the fitness of an instructor. This is just plain ludicrous. Rather repeat the advice to them that they are not obliged to fly. They are the PIC and thus the authority.

FIs are working under pressure to perform, both pressure from their training organisations, from their students and from themselves to earn a living. The question Marcia Nunes asks is very relevant. But I don't see that she proposes a "regular construct". You can't regulate the fitness of CAT pilots either. Would you rather have no work time regulations for them and instead trust their "self-assessment"?

FI fatigue and airline pilot fatigue are two quite different things because of the different type of operations that are conducted. An airline pilot may conduct three/four T.O.s and landings in one day? An FI may do 10 in one training session, in a busy airport environment, with an underperforming aircraft (depending on the time of year), and a student who (unwillingly) may be trying to kill him.
Extreme temperatures are a factor. If you are operating in Rome during the summer for example, the temperature in the cockpit of an aircraft that has been on the ramp for an hour will easily reach 50°C. And, except for the Cirrus, most training aircraft do not have air conditioning. If we add to this that, to save money, most airport managers and ATS providers have reduced the operating hours of many airports all over Europe, the ability to ground a fleet during peak temperature hours and flying later in the day (especially during summer) becomes impossible. In these conditions, you try to tell an accountable manager or HT to keep his aircraft grounded between 13:00 and 16:00, see what answer you get.
My point is that this topic is much more complex than what would first appear to be. There are virtuous organisations and instructors who self-regulate, but there are also many more which do not. There are also countries that have had FTL rules in place for instructors (ENAC Italy is one of them). They are no longer official, but still used as benchmark guideline. Maybe [~246] you could start looking into this?
I do however agree that over-regulating is not the solution. Rather promoting a culture of common sense and safety awareness (real safety awareness, not the ticking of boxes required by the regulations).
Another problem is that many flight schools pay pilots by the flight hour, so if you do not fly, you do not earn. This, in my opinion, does not promote safety.

I am not talking about pilot fitness of course, I am talking of ATOs planning their instructors with reference to rules that are only feasible for CAT pilots.

To my knowledge, not one ATO that I know, or have worked in does this.

You are absolutely and 100% correct [~19839]. No intention to over-regulate. But regulate never the less. In Portugal, there were also some rules, which are no longer official as well. But no Accountable Manager will accept limitations that EASA itself is not imposing. So...

Do agree, and this is a problem in Europe. Also true, no one wants to over-regulate. However, for me there is a key word, and that is Safety (notice the capital S. Did not want to overdo it with all capitals).
What accountable managers need to understand, and this can sometimes be difficult because they may be managers but not pilots, is that - even in a training environment - one accident can do more damage than anything else.
Does EASA have any accident data on flight instruction? The NTSB certainly does and it would be interesting to research how many accidents have been attributed to fatigue in Europe.
In the end, for now, it all comes down to virtuous behaviour and examples set by Postholders. And there are some. If this culture and mindset are encouraged, then we've already gotten off to a good start.