Which change can make blue relatively warmer while keeping it within the same colour family?

Correct answer: Shifting it toward green

Colour temperature is relative, not an unchanging property. A blue shifted slightly toward green is generally warmer than a blue shifted toward violet, because green lies nearer the warm yellow side of the colour wheel than violet does. The hue remains recognisably blue, so option C is correct. Violet makes blue cooler, while black and white mainly change value and do not establish the intended warm hue bias.