You have literally no idea what you're talking about. The friction of the cable rolling through its various touchpoints would be far hotter than anything any ambient temperature is going to throw at it, regardless of where the system is. Friction don't care if its in Florida or Colorado. The hottest ambient temperature is going to be is what, 110? BFD.
delta_T=(7800*mu*Wab*v)/(J*(k1+k2))
delta_T = rise in temperature
mu = coefficient of friction
Wab = surface energy of adhesion
v = sliding speed
J = mechanical equivalent of heat
k1, k2 = heat conductivity of the two materials
In other words: If the cable can handle it in any other location, it doesn't matter that this is in Florida.