The I-V characteristics of materials and devices should always be measured at the same thermodynamic conditions, i.e. at the same temperature. Mixing the actual isothermal I-V characteristic with the temperature dependence doesn't lead to any useful data for the purposes of physics (but it is occasionally done in electrical engineering and electronics design for certain parts like NTC heaters and breakers).
A pure semiconductor at a constant temperature would be a pretty good Ohmic conductor, i.e. the current will be proportional to the applied voltage. This is a lot harder to measure properly on semiconductors than on metals, though, because of junctions formed with the metal wires that one has to attach for the measurement.
The conduction characteristics of semiconductor devices with one or multiple different materials forming junctions, on the other hand, is highly non-linear and can be made very complex. These devices will also have a temperature dependence, but it can be tuned very finely with appropriate material combinations and geometries.
Pure metals have typically increasing resistance with increasing temperature, but alloys can be made that have almost constant temperature characteristic (i.e. they are both Ohmic and temperature independent). One can also make metal alloys with negative characteristics, if necessary. Both constant and negative temperature characteristic is of enormous importance for the design of electronics, almost none of which would function properly if we couldn't make these near zero-TC metal alloys for resistors and NTC's for temperature measurement and compensation.
Non-metallic materials with very strong negative temperature characteristics often use percolation phenomena, i.e. on grain boundaries in sintered crystal powders, where conduction can only happen in very few narrow points in the material. As the material expands, these points of contact may get lost and the resistance may increase by many orders of magnitude over the technical temperature range of the material. The physics of these systems is very different from that of metals and semiconductors.
I think it would be better to say that power lines are designed to avoid ohmic heating rather than that they make use of it. I am not sure about the potential advantages of the heating for lines that may otherwise be weighed down and damaged or destroyed by snow and ice in cold climates, though. One would have to look at the design requirements for these power systems to understand if their designers make explicit use of these otherwise unwanted losses.
You are correct that one can trade current for voltage and vice versa by adjusting the resistance in circuits. Much of electronics design is a repeated application of that principle.
As for the question of how to design materials that have nearly temperature independent characteristics, that would require a very deep dive into solid state physics and materials research and I will leave that to someone who actually has the necessary detail knowledge. The guiding principle in many of these practical applications is that one tries to offset a positive gradient of one material with the negative gradient of another or one tries to combine multiple materials in such a way that the physical effects (like the formation of defects in the mixed material) offset bulk effects like the increase in the number of conduction band electrons in either of the constituents.
So, is there any macroscopic physical meaning to this statement that the negative temperature is "hotter"? Doesn't this mean that the negative temperature required for that laser to exist ought to be so "hot" no mere mortal can handle such a device?
If you go far up enough in the atmosphere, you'll reach regions where the temperature is over 3000 K. Yet rockets aren't exploding in flames when they get there, because the atmosphere is very sparse. It will transfer energy to the rocket, because its temperature is very high, but only incredibly slowly.
In general, human beings cannot detect temperature; we can only detect heat transfer. This is why metal surfaces often feel cold; they're the same temperature as everything else, but they conduct better, so you lose heat faster when touching them. Similarly, if you go up really high into the atmosphere, you won't feel like it's hot. Instead, you'll feel nothing at all.
So our intuitive sensory notions of "hot" or "cold" have very little to do with temperature. So it's indeterminate how "hot" a negative temperature system will feel, because that depends on how quickly it transfers heat to your body. All the temperature means is that it will transfer heat.
Best Answer
This DTIC Report (PDF) shows that the conductivity of silicon continues to increase as temperatures increase from 500K to close to silicon's melting point at 1,687K:
This is due to the rapid increase in the number of free electrons and holes with increasing temperature.
As temperatures increase, phonon scattering increases and this reduces the mobility. The rate of increase of scattering with temperature is much less than the rate of increase in free electrons and holes with temperature. Hence, conductivity continues to increase as temperature rises.
Intrinsic vs extrinsic
The plot below, from the same report, shows how the conductivity of intrinsic silicon (samples 5 & 6) compare with doped (extrinsic) silicon (samples 1 and 2). Note that, unlike the plot above, the scale of the top axis on the plot below is in centigrade, not Kelvin:
At low temperatures, the doped silicon has higher conductivity than the intrinsic silicon semiconductor. As temperature increases, the conductivity of the doped Si drops slightly to due increased scattering. As temperatures increase further, the growth in thermal carriers becomes more important than the increase in scattering. As temperature increases further, the conductivity also increases.