Twice I have experienced this event.
Flying F/L 370 with sat -45degreesC when temp increases to 0 degrees c.
Boeing have a QRH checklist for this.
No auto throttle, no EPR.
No TAT. Set power and fly attitude. Usually max contin. N1 to hold altitude.
Fits the scenario of "Ice Crystal Icing" or ICI. When it's sufficiently severe, it can ice up the TAT probe - the combination of probe heat/melting ice gives the 0 degrees C (and on EPR engines, often the inlet probes, hence bad or no EPR). Supposedly, above 30k it's too cold for super-cooled droplets to exist - instead you get ice crystals. They bounce of cold surfaces but melt and stick to heated surfaces (e.g. probes) - the first crystals melt, but in high concentrations the new crystals re-freeze the melted water and the probes can ice over (also can form ice in the engines which has lead to flameouts when it sheds). TAT probes are particularly susceptible to ICI icing since you can't throw too much heat in without affecting the measured temperature. Pitot probes don't have that problem and have lots of heat. Hence ICI icing of pitot probes is rare, but it has happened (AF 447 being a tragic example).