It has been proposed that entangled two-photon absorption (E2PA) can be observed with up to 1010 lower photon flux than its classical counterpart, therefore enabling ultralow-power two-photon fluorescence microscopy. However, there is a significant controversy regarding the magnitude of this quantum enhancement in excitation efficiency. We investigated the fluorescence signals from Rhodamine 6G and LDS798 excited with a CW laser or an entangled photon pair source at ∼1060 nm. We observed a signal that originates from hot-band absorption (HBA), which is one-photon absorption from thermally populated vibrational levels of the ground electronic state. This mechanism, which has not been previously discussed in the context of E2PA, produces a signal with a linear power dependence, as would be expected for E2PA. For the typical conditions under which E2PA measurements are performed, contributions from the HBA process could lead to a several orders of magnitude overestimate of the quantum advantage.