Cecco
Yes a stuck open engine anti-ice valve would give that sort of split. But when you said it happened after an HSI that is the major clue.
4 or 5 years ago we had an HSI done on one engine of our Citation 2. (different engine I know). After the HSI the ITT was 40 hotter than before. The overhaul shop said it was in limits and it was just bad luck. After about 30 hours we demanded an investigation and the LPT blades were clipping the shroud ring. I am sure if we were paying the bill the LPT blades would have been scrapped but as the overhaul agency were paying they managed to crop the blades! After the temp went down 40.
Another question: are the two fuel flows identical and what are the 2 fuel flows at identical temps? It could be that a temp probe has gone short circuit.
I would not be happy with this situation, there may be something wrong inside that the company that did the HSI company will refuse to rectify if it is left too long.
This is a very good shout!