## 1 Introduction  
Optimizing a premature neonate's thermal environment is still a challenge in routine clinical care. There are several reasons why poorly effective thermoregulatory responses to thermal changes increase the risk of thermal stress in preterm infants. Firstly, the level of basal metabolism (when expressed per unit of skin surface area) is lower in preterm infants than in adults. Secondly, the sweat glands do not operate effectively in infants with a gestational age below 30 weeks [1]. Thirdly, there is evidence to suggest that immature neonates' peripheral vasomotor responses are impaired during the first few hours after birth [2; 3]. Fourthly, the skin's high permeability increases evaporative heat losses. Lastly, body heat exchanges with the environment are larger in infants than in adults as a result of the high skin surface area/body volume ratio and the body segments' high degree of curvature.  
Optimal thermal conditions are generally defined those resulting in a core body temperature of between 36.5 and 37.5 \({}^{\circ}\)C [4]. Heat stress (corresponding to a core body temperature above 37.5 \({}^{\circ}\)C) can result from increased body heat storage caused by (i) over-insulation from excessive clothing, (ii) high environmental temperatures, (iii) fever and/or (iv) immature, inefficient thermoregulatory processes.  
Body overheating can also occur if a neonate is wrapped in a plastic bag at birth [5,6]; indeed, several researchers have called for further research into the effectiveness of this procedure [5,7,8]. When heat stroke (extreme body temperature \(\geq\)40 \({}^{\circ}\)C) occurs, cell damage leads to coma, shock, convulsions, severe neurological impairments, kidney failure and haemorrhage [9].  
The World Health Organization defines cold stress as a core body temperature of between 36.0 and 32.0 \({}^{\circ}\)C. When exposed to low ambient temperatures, the neonate reduces its peripheral blood flow and increases the metabolic heat production. This mechanism decreases the energy available for tissue synthesis and thus impairs body growth. The increase in the metabolic rate induces hypoglycaemia and blood acidosis through the release of lactic acid. Prolonged cold exposure is life-threatening. For example, [PERSON] et al. [5] reported that the odds ratios for late sepsis and death respectively increased by 11% and 28% for a 1 \({}^{\circ}\)C decrement in admission body temperature. In summary, the pathological effects of thermal stress in neonates are particularly devastating, and include severe impairments in neurological development and body growth.  
Here, we review the strengths and limitations of models used to both predict the optimal thermoneutral incubator air temperature (T\({}_{\text{inc}}\)) for nursed neonates and avoid the risk of thermal stress. Ideally, a model should incorporate all the variables related to body temperature regulation. However, given the complexities of the body's thermoregulatory system and the simplifications needed to describe the various heat transfers between the skin surface area and the environment, care providers do not yet trust these models to make accurate predictions.