Anything is possible.
My Speedstream 5861 runs very hot, but that does not affect performance. It does shorten the life of the power supply.
Currently I use a Westell 2200. It runs moderately hot. That doesn't seem to affect anything (yet).
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I have had problems with an older computer (no longer in service). It would overheat, and apparently push some component outside its normal operational range. It required power off/ power on to get it working again. When this sort of thing happens, it is typically a single component that is excessively sensitive to heat.
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My guess: I suspect that the technician is spinning a story -- especially if he diagnosed remotely. But it wouldn't hurt to pick up another modem from eBay. If the problem occurs with a different modem (preferably different model entirely), then that would pretty much rule out modem problems and point to line woes or house wiring problems.