Like Bleve and others I've seen temp rises in the order of 20-30 degC passing through the ITCZ between Japan and Australia on many occasions. Usually the first thing I'd notice is that the aircon can't deal with it and you can smell/feel the cabin air become more humid and then notice the SAT rising rapidly. A good reason not to operate right up at or above optimum in that neighbourhood. Once out of the hi-temp area the SAT decreases just as quickly.
Diversions around thunderstorm activity of well over 100nm are not that uncommon in oceanic airspace, I've done plenty over the years.
Regards,
BH.