Dissipation in watts for a linear regulator is (Vin - Vout) x I
The higher the input voltage the more power must be dissipated as heat.
Corrected: you forgot the brackets.
Yes, the higher the input voltage, the higher the power dissipation.
Although it's usually negligible, the current flowing out of the regulator's 0V pin can be significant too. Especialy in low drop-out regulators, when the output voltage is fairly close to the input voltage. This normally isn't a matter for thermal design. It's more important when dealing with power consumption.