The heat transfer process from a 6.4 Watt blue light flexible phototherapy mattress to a human hand has been studied. The intended use of the mattress is the provision of neonatal jaundice phototherapy during Kangaroo Mother Care (KMC) or skin-to-skin care. The heat transfer process has been studied with temperature and heat flow sensors inside an expanded- polystyrene spheroid 25mm of thickness where the phototherapy mattress's non emitting surface is in contact and folded around the hand while the light radiates outwards, to the polystyrene spheroid. The effective thermal capacitance of the phototherapy mattress was calculated as 3.4 J/oK, the mattress-to-hand thermal conductance was found to be 0.25 W/oC, the maximum temperature gradient between the mattress and the palm of the hand was 10oC and the maximum power absorbed by the hand, 2.5W. The palm of the hand skin-to-core temperature gradient was 0.5oC. It is expected that when used in KMC only one half of the hand skin surface would be in contact with the phototherapy mattress so that the effective thermal conductance to the hand in this conditions would be 0.125 W/oC. Further study is suggested to include sweating effect of the hand.