The spectral sensitivity of a concentrating triple-junction (3J) solar cell has been investigated. The atmospheric parameters such as the air mass (AM), aerosol optical depth (AOD) and precipitable water (PW) change the distribution of the solar spectrum in a way that the spectral, electrical and thermal performance of a 3J solar cell is affected. In this paper, the influence of the spectral changes on the performance of each subcell and whole cell has been analysed. It has been shown that increasing the AM and AOD have a negative impact on the spectral and electrical performance of 3J solar cells while increasing the PW has a positive effect, although, to a lesser degree. A three-dimensional finite element analysis model is used to quantify the effect of each atmospheric parameter on the thermal performance for a range of heat transfer coefficients from the back-plate to the ambient air and also ambient temperature. It is shown that a heat transfer coefficient greater than 1300 W/(m2 K) is required to keep the solar cell under 100 °C at all times. In order to get a more realistic assessment and also to investigate the effect of heat transfer coefficient on the annual energy yield, the methodology is applied for four US locations using data from a typical meteorological year (TMY3).