Ramp up time is related to the Specific Heat Capacity of the metal, the mass of the wire, and the amount of current flowing through the wire which is related to its resistance.
If dealing with the same type of metal, Kanthal for example, then the Specific Heat Capacity remains the same, but the mass will influence the resistance therefore influence the amount of current that is passed through assuming the same wattage.
When dealing with different types of metal, N80 vs Kanthal for example. Using the same dimension of coil (amount of wraps, ID & gauge), N80 has a slightly lower Specific Heat Capacity, but that is over come by it’s much higher mass. However, for the same dimension of coil, N80 also has a lower resistance therefore more current will be passed through the coil for the same wattage – hence why it heats up faster.