that's relatively simple.
imagine that your max take off thrust available depends on outside air temperature. it's flat rated (=constant) until a certain temp (e.g. ISA +15C) then decreases linearily with temperature to maintain constant turbine entry temperature.
given this, you may understand that you can take off a certain aircraft gross weight until a certain OAT. got it?
imagine now you are at low OAT but you have a GW which permits take-off at ISA + 40C. then you can tell you thrust control to compute the take-off thrust at the assumed temperature of ISA+40C, and you will obtain the thrust required for the take-off.