A system for heating an aircraft surface having a thermally disadvantaged zone includes a carbon nano-tube (CNT) sheet heating element having a power inlet configured to receive power from an external electrical power source and provide it to the CNT sheet heating element that extends across the thermally disadvantaged zone. The CNT sheet heating element is configured and arranged such upon application of power from the external electrical power source to the CNT sheet heating element, the CNT sheet heating element produces a first heat output in a first zone and a second heat output in the thermally disadvantaged zone with the second heat output being greater than the first heat output.