Final answer:
The spectral class K signifies the coolest stellar surface temperature among the options provided. K-class stars are cooler than G, A, and B-class stars in the spectral classification system.
Step-by-step explanation:
In the context of stellar spectral classifications, the classification signifies the star's surface temperature—ranging from the hottest to the coolest. The given options are B, K, G, and A. By examining the order of the spectral classes, which are O, B, A, F, G, K, and M (with L, T, and Y for even cooler objects), we can determine that the coolest stellar surface temperature among the given options is signified by spectral class K. This is because K-class stars are cooler than G and A classes and are only warmer than M-class stars, which are not listed among the options.