The single-beam Z-scan thermal lens technique is conducted to evaluate the fluorescence quantum yield of various solutions in the case of high-moderate absorption, considering both scenarios: solutions with substantial fluorescence and solutions with high thermal efficiency but low fluorescence. An analytical calculation is performed to determine the uncertainties associated with the random errors introduced by optical detectors. The results reveal that solutions with low fluorescence lead to a significant error, whereas higher fluorescence can help in decreasing the uncertainty. Additionally, the issue of random errors arising when multiple measurements are needed to accurately estimate the fluorescence of a solution will be discussed in different situations.