My first thought was that as the temperature creeps up to (and even past) the "design day" conditions, the electrical grid sees an extremely high load, which could very well yield brown-outs or slight dips in voltage. Those dips could affect the 1070's power supply, potentially causing the unit to generate more heat (draw more amperage to achieve the same power levels). Extra heat could be just enough to cause heat-related problems, and the solution then could be tracking the temperature above the unit for a few days and providing a bit more ventilation if necessary. However, I'm a little suspicious of that scenario since your PC's UPS didn't report any appreciable change in input voltage, so that avenue of investigation may not be worth your time.

Your idea of isolating the cable is a good one - if you cut your system off from the cable and the 1070 gets through a hot afternoon successfully, you might consider a new box or a filter of some sort for the cable line. You might even tell your cable provider that the noise on their system is bad enough to cause disruption in other electronics in your house - they might cough up an RF filter of some sort.