Re the apparent low-power take off; - the take off run appeared longer than normal.
Assuming that the TAT probe was the errant device; is TAT used in the calculation of thrust in the MD?
In some aircraft, TAT is used by the thrust management computer. If the TAT value is erroneously high, it can give a low thrust setting. The crew should cross check the demanded value with that required; if TAT is at fault, a manual value can be entered for computation or the required thrust level set manually.
This problem was often seen with non aspirated TAT probes which detected radiant energy from hot concrete surfaces.
Low power could contribute to low speed immediately after take off if normal pitch attitudes were used, i.e. attitude for the initial climb as opposed to speed, or before a speed schedule was reached.
Extending the speculation, then if the aircraft would not, or was judged that it could not continue to fly, then the landing should have been relatively ‘straight ahead’ (~ crosswind). However, if the low speed situation resulted in loss of directional control (wing drop) then a more severe veer-off might result in an ‘off airport’ landing.
Is the standard MEL practice for isolating the TAT probe via a breaker, if so what breakers are adjacent to TAT?