Just bought the BenQ HT3050 - I have a few questions.
Definitely try out another cable. There haven't been reports of HDMI-port issues on these models (and as AV says, the newer HT2050/HT3050 has a less recessed, more typical HDMI housing than the old W1070).
For cooling, you could run in High Altitude Mode if you want, which cools the projector aggressively at the expense of lots of fan noise (all 4 fans fire at full blast).
But then you sacrifice the relatively quiet operation of these units (which is one of their strengths) for no good reason :-)
If the unit isn't shutting itself down, you've got nothing to worry about: lamp-based projectors do indeed normally run hot.
BenQ HT2050 Projector; Kodi (on Ubuntu, OpenELEC & S802) via Sony STR-DH540 AVR with Boston Acoustics SoundWare XS SE 5.1 Audio + Jamo 210 Sub. Emby for Mobile Streaming.
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