I opened it!
As
Shock &
sunnyhighway suggested I tried to remove the trigger; suddenly I heard a crack from inside and a clip fell out. 10 minutes later I could remove the right cover.
The cover are held by a bunch of internal clips
(red circles), two of them are now broken. A lot of screws are holding in place the thermal unit.
The metal frame around the LCD is held by screws on the bottom (together with the PCB) and with solid metal clips on the top
(blue arrows). The frame is not just a sheet of folded metal, I think it's cast metal; anyway it's very solid.
Note there is no puch button for the trigger! Insteas testo uses a reed relay
(pink circle) and the magnet sits on the trigger!
In the next couple of days I will try to repair the thermometer; the display always shows that the temperature exceed the measurement range (too hot).