Last Monday (May 2nd), the conditions at the 2.5 mile High Plains Raceway track in Byers Colorado, was 37F degrees when the track went green at 8:00 am, and reached only 53 degrees by 4:00 pm. The sun occasionally peeked from behind the cloud cover, but was mostly partly cloudy to overcast.
I exited pit lane and blended into turn 2 at about 8:20. I wore a turtle neck undergarment, and was generally warm and comfortable but had to keep the face shield partially open to prevent excessive fogging.
My first laps were on cold pressures 36F 42R. This was way too high, a little slippery, so I returned to the pits. I dropped the pressures to 30F 30R. This was decently grippy but felt squirmy in turn 4 and elsewhere, so I returned to the pits after just two laps. I increased the pressure by 3-4 pounds in each tire. This is was the best compromise between grip and stability.
I was on brand new K3 sticker tires, both ends. I probably only ran 25-30 laps all day, my physical conditioning not at peak.
No tire warmers, the K3's warmed up by two laps, or a little less.
So I thought they worked decently well in colder track temps. I don't think you'll be able get enough heat into them on the many slow turns of the Tail of Dragon to get them really sticky, although if the sun is out and maybe even if it is not, there should be enough grip to easily get the knee down I would think.
I've been very satisfied with Dunlops on other bikes. My main reason for going with the K3's again is confidence. It's not just about being grippy, but also having the right profile, the right flex in the carcass so that it works in harmony with my suspension setup, and communicates good feedback.
Be careful with the K3 in the wet. There's no tread at the edges so it behaves like a slick, with no channeling groove for the water to escape.
I also agree with others, not to run them too far. They seem to lose grip before they lose tread depth. The carcass is so thin, the tire so lightweight (especially the rear), there is truly only a couple of millimeters (at most) of rubber vulcanized at the edge. The edge goes away before the center, especially on the track, but also on the street if you do lots of curves. It's an expensive tire to run with.
Below is the aforementioned track day pic. If I have a concern, it's not so much cold weather performance but how long it will hold up at higher temps and extended running.