Hm. This is a puzzle, and I do like puzzles.
Do you get vigorous boiling water from the group head (aside from the readings), or does it just pour out?
Aside from the likely inaccurate thermometer, assuming that it is giving relative readings, the group temperature should not be a lot cooler than the boiler water when first run with an unflushed HX.
I was pondering how this could be, and I finally found a diagram for this machine (well, the BZ99, but the BZ99 and the Livia 90 are the same, according to many searches). Refer to
http://bezzera.it/pdf/BZ99_GB.pdfPage 11 has the boiler on it.
The HX is a cup shape, with fresh cool water entering from the top (via part #4, 5) and hot water leaving from the bottom through a dipper tube (part #2).
What if this dipper tube had corroded off, or developed a hole, or failed in some other way - you would have cold water entering at the top and leaving at the top.
Have you looked inside the HX?