There are at least two separate issues to consider here.
Minimising brake wear over the life of the brakes, to do this follow your SOPs which will no doubt be guided by the information in the video above.
The other issue is simply keeping the brake temps within FCOM limitations for takeoff.
While these two considerations will ideally be managed together, if you are simply trying to bring down the brake temperatures so that you remain within takeoff limitations once taxi has commenced, simply keeping your speed lower will help. I'll try to explain why.
Looking back to the kinetic energy formula: Kinetic energy of KE = 1/2 MV(squared), V is the only variable that can be controlled, short of offloading pax, fuel or freight. Having said that, it has a disproportionately advantageous effect on reducing the the brake energy demand and hence keeping the temps below TO limits. For the mathematicians, brake energy required is proportional square of taxi speed. So if you halve the average taxi speed then you input a quarter of the brake energy.
Whilst this specifically runs contrary to minimising brake wear as such, there are some circumstances where it is hard to avoid and this will get you airborne without exceeding any limitations.