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.
You can get thrust changes. Are you sure the thrust ref didn't reduce toward and beyond the thrust required even to the point that you had to select climb thrust and in fact increase thrust at that point, because everything you describe including selecting climb or even cont thrust is still screaming TAT probe icing to me. I'll see if I can find some reference material from a QRH.
EDIT
Note; not Airbus material
One or more of the following may be evidence of TAT
probe icing:
•The autothrottle disconnects and the
reference/target EPR and reference EPR displays
blank
•The thrust levers are not aligned with the engine
EPR displays
•The engine EPR displays are not aligned with the
thrust levers aligned
•A decrease or increase in the reference/target EPR
displays at a constant altitude and speed
•The engines are unable to achieve the maximum
continuous or the maximum climb rating with thrust
levers fully forward
•The TAT display remains constant and near 0
degrees C during climb, cruise, or descent