How much one should warm up before running a 12km...?

No warmup: The idea is endurance not pulse running like a 100mts run. So save your energy, take lot of rest, and do some stretching just before the start. Use the initial run as a warm up by slowly increasing the pace. Increasing warm up can tire you up. All the best.

Controversial: Some recent studies even questioned the ability to prevent lesions and/or increase performance of warm-up. Plus, it is hard to define (how, what muscles, how long, etc). Therefore, fixed rule does not exist, (scientifically supported and universal). I think the optimal point varies for each individual. Be careful, keep doing healthy activities, and thank you for giving us the chance to discuss it.