This is an old thread but still a reasonable question left unanswered.
I have torn down and built up a few compressors and am currently writing a detailed shop manual for the Yong Heng compressor (compressors in general work about the same). In the process of doing so I have run temperature gauges on every major component and logged a lot of data.
With time the motor is subject to "heat soak" and continues heating internally, making it less efficient and causes it to generate more heat from the same workload. Of course in a simple system as the tank pressure rises the workload increases and also contributes to heat generation. The fan on the Yong Heng is insufficient to run the compressor continuously, so if left on eventually the enamel on the windings will break down from overheating and windings will start shorting together which decreases work output and increases current draw, making the motor less efficient and causing it to heat faster. The solution is to add a large external fan to cool the motor; when doing so the motor tops out at about 68°C.
In most setups oil cools the primary cylinder and piston. In the Yong Heng setup there isn't a good mechanism to cool the oil and it will continue to heat with time. Oil in the YH splashes against the housing which has a lot of surface area but little air flow and not much thermal conductivity. Adding an external fan to cool the housing will help, but the oil is still subject to overheating due to the housing's lack of thermal conductivity. When the motor reaches 68°C the oil will be about 58°C depending on the setup. One thing to note is the YH has a lot of first-stage blow-by which escapes out the cylinder housing vent; as such the compressor should be used in a well-ventilated area.
Using a 6-gallon bucket filled with ice and then adding water plus use of the aforementioned fans will allow the YH to run for about 1.5 hours continuous in a 18°C environment. The 0°C ice water cools the second-stage cylinder so less heat is transmitted to the first-stage cylinder, keeping the oil cooler. The first-stage cylinder has limited cooling if the pressure-shutoff relay is installed as it blocks the air flow path.
Some dive tank fill station compressors have three, four, five, or six stages, but they still operate somewhat the same in principle. The main differences compared to the YH are in additional complexity, efficiency, and maintainability, not to mention initial cost. The YH is extremely simple and cannot sustain commercial usage, but is well suited for the low-volume weekend shooter. Competition shooters probably want to either have their tanks filled at a dive shop or purchase a quality low-volume dive compressor and 6800 or 9000 PSI microbore lines. Even then bad crimps can lead to blowouts, so care must always be taken.
