Basically, one measures the absorption as a function of wavelength: the total integrated absorption (over wavelength) gives you the negative logarithm of the transmission. The transmission is the fraction of light that passes so 1-T gives you the part that is absorbed. Therefore, if you know the incident intensity (J/(m2 s) you can calculate the absorbed heat.
Pitfalls: (1) also scattered light (not absorbed) contributes to the loss of transmission and (2) you only will get the energy lost with the band of wavelengths that you studied.
Oops, you are right . I misread the question, maybe. But there is a quantity known as the Heat of aDsorption that one could possibly obtain from a spectral line that changes with the amount of aDsorbed mass. A Heat of aBsorption is no other quantity than I described. The relation between the two is found from the correlation. But this I never did in one way or another.