Plugging the card out and back in didn't solve it. I've now tried something else. When I did the initial configuration I turned "Television" and "Recording" of the analog receiver of the Pinnacle PCTV-310i to "false". I now turned it back to "true" - no shut off so far. See Television->Capture Cards in MediaPortal-Setup.
Maybe something in the code had changed since 0.1.3.0, when I first configured MP.
To make a long story short: I got the problem solved when I enventually changed back from the PicoPSU to the original Silverstone PSU. No more reboots, but fan noise is back....