Several years ago, I had digital cable from Time Warner. The box ran hot, but nowhere nearly as hot as Zenith2134's. I did not have the box on top of my TV; the converter was on the lowest shelf of my entertainment unit (which now is occupied by my DVD player). The box, a Motorola STB, worked extremely well the short time I had it (a couple of years) before digital cable rates went up. I now have bare-bones basic cable running more or less directly to the set (local channels only, plus WGN America, C-SPAN 1, and a couple of religious channels, to say nothing of QVC) and no problems whatsoever with heat buildup from anything.
Every once in a while I toy with the idea of dropping cable and getting a DTV converter box, but every time I read about these boxes getting exceptionally warm (and failing within six months or so) I forget about it. I don't honestly think a DTV box with rabbit ears would work in my situation anyway, as I live in an apartment building and cannot use an outside TV antenna. Rabbit ears, unless they are the expensive amplified kind, won't work here either (and even if they did work at all, it probably would be a crap shoot as I will explain), because I'm some 45 miles from the Cleveland TV stations. It's ironic because my FM radio reception here, using an external Terk "tower" antenna atop my desk with my stereo system (and the built-in whip antennas on my FM portables, to say nothing of short wire antennas on my vintage FM radios), is excellent. I guess the difference is the all-or-nothing nature of DTV signals, and the fact that they are far weaker than FM radio stations.
BTW, why is it now impossible to hear audio from channel 6 TV stations on 87.75 MHz? (Back in my old neighborhood, long before DTV, I used to be able to hear channel
eight audio at the bottom of my FM dial.) I thought the sound carriers of digital television signals were on the same frequencies as the old analog ones, unless the DTV stations are on UHF channels. I always thought that the audio carrier of, say, channel six would be 86.5 MHz (4.5 MHz above the lower edge of the channel), regardless of whether the signal was digital or analog. Why I was getting channel 8 audio on 86.5 MHz, however, is still a mystery to me, even to this day, since the sound carrier for that channel is (or was, with analog TV) 184.5 MHz. I was living in a Cleveland suburb at the time that was perhaps 30+ miles from the stations. Hmmm.