Airbus' write up about the problem was that the heating in the TAT probes,at times, may be insufficient & lead to the probe icing up followed by the ice rapidly heating up giving false TAT & SAT indications.
I think you will find that TAT probe icing will give the illusion of increasing SAT plus some other nasty symptoms.
ISA and max altitude and coffin corner
Note the question about TAT use in the ADC, if true then more than the airspeed indications might be affected – ADC comparator and consequences, use of ADC/TAT in IRS component of ADIRS, ADIRS comparator and consequences, - rudder limiter, cabin alt, etc, etc.
Reading all this not as a pilot but a certified engineer I'm shocked and astonished, if in today's highly automated airplanes the TAT & IAS probes deliver the most fundamental data to all kind of essential systems, while them self being prone to failures as shown above?
Are TAT & IAS probes the Achille's heels of today's computerized airplanes?
If their data is so essential, should we not have a truly redundant system on board, that also can measure speed relative to the surrounding air but use a different method?