I think that temperature can be ruled out. Leaks due to temperature are more likely during hot weather, or after the ink freezes. Your circumstances do not fit either of these cases.
Increased temperature reduces the viscosity of the ink, so that by capillary action it is sucked into and through the narrow gaps between the plastic tube and the nib section or between the ball and its housing. Ink is mostly water so it expands when it freezes. Expansion can rupture the plastic tube, or permanently deform it so that it no longer fits tight against the nib section. When the ink thaws again, it seeps out of cracks in the tube or the larger gap where it connects to the nib.
The most likely cause which I can think of is a mechanical or design fault relating only to the black pen into which the refills are inserted. This would explain why changing the brand of refill makes no difference - although it is possible that different brand refills are in fact obtained from the same manufacturer - seePrivate Label. You could test this theory by inserting blue refills into black pens, and vice versa.
A post on Quora, Why does the Reynolds Trimax refill always leak? attributes the leak to the cap :
I figured out that the cap on the refills pushes air into it, effective breaking the seal and making the ink come out. I've even verified it. I took two refills and made a hole in the cap of one of them. Then I removed the caps from both of them multiple times. I found that the refill with the hole in its cap didn't leak no matter how much I uncapped it, but the refill without it leaked in 15–20 removals of the cap.
Gel pens dry out quickly, so it is necessary to store them with the cap on. A blog by supplier pens2order explains :
Like all writing instruments, gel pens do have their quirks.
If the cap is left off for too long, the ink will dry up in a relatively short amount of time, something which rarely if ever happens with ballpoints. The cap of gel pens contains a tiny silicone ball, which when placed on the pen, forms an airtight seal which prevents the ink from drying out.
When a cap is pressed onto a pen this traps and compresses a volume of air between the cap and the pen. Increased air pressure forces back the ball of the pen, as when you write with it. This allows ink to flow out. I presume that the silicone ball mechanism allows most of this excess pressure to be released, allowing an airtight seal to be made while minimising air pressure inside the cap. It is possible that there is a manufacturing fault in the caps of the black pens which you use, but not in the caps of the blue pens, so that the silicone ball mechanism is not working as it should in the black pen caps.
However, it is difficult to see how this explanation would fit with your observation that the pens leak in winter. Silicone rubber expands more than polypropylene from which the cap is made; the coefficients are about 340 and 90 ppm per degree C. So the seal made by the silicon ball should be tighter in summer and looser in winter, suggesting greater likelihood of leaks in summer - contrary to your observation.
It is also difficult to see why the blue cap would not contain the same fault. Presumably both are made by the same process, and any colour distinction is added afterwards. Perhaps there is a difference in the colour of the silicone ball?
The Japanese company Sakura invented the gel pen in the 1980s and has this to say about Gelly Roll pen care :
It is very important to put the correct cap on the pen between uses ... In our Gelly Roll ink system there is a tiny silicone ball inside the cap that touches the tip and helps prevent any air from drying out the gel in the ball chamber when the cap is on.
This explains that the ball provides a seal at the pen tip, and does not act as a kind of valve regulating air pressure in the cap, as described above.
Another Sakura FAQ explains why its Pigma Micron pen is prone to leaks because of an air vent collar.