For MD 80´s powered by JTD9-219 engines, yes there is a minimum assumed temperature for flex TO.
This comes from an specific system call ART. When reducing thrust for TO, ART must be off and that means that the full power is available for the ATM ( assumed temperature).
When OAT and ATM are close, EPR max for ATM might be higher than EPR norm for OAT.
At sea level and ISA engine output is 21.000 lbs (ART auto) and 21.700 lbs for ART off.
At SL and OAT 26ºC EPR norm (TOGA/ ART auto) is 1.93.
If ATM is 35ºC, EPR max (flex TO/ART off) is 1.94.
Therefor ATM must be higher than 35ºC to perform a real thrust reduction.
REGARDS