amc890
If the rapid rise in displayed temperature was due to TAT probe icing then I would expect that there would be no change in engine thrust. If the outside air temp remains constant, then the Flight Level remains constant and there is no requirement for extra thrust. However as explained previously, if the OAT does increase, there is a need for increased thrust.
In the event I described, the thrust did increase - significantly. In fact we reached max cruise thrust and had to select climb thrust to maintain Flight Level and speed. That is consistent with a real increase in OAT, not a false reading due to TAT icing.