Yes, but it's negligible in the desired temperature range ~20C.
To raise temperature of the wire by 20C requires 0.5A and guess a linear amp/heating scale is probably close enough for this application.
The basic circuit will be an11R, in series with the Nichrome element and +12v supply. PWM the voltage through a logic level n-channel MOSFET Gate, -ve side of heating element to Drain and Source to GND. This gives ~1amp to play with, but I need to calculate the requirements for raising the temperature of the glass. A variable resistor in place of the 11R will provide more power flexibility.