In the next run, the elongation of the complementary strand will linearise the hairpin separating the fluorophore and quencher.
Dark quenchers offer a solution to this problem because they do not occupy an emission bandwidth.
The quencher then returns to the ground state through emissive decay (fluorescence) or nonradiatively (dark quenching).
In nonradiative or dark decay, energy is given off via molecular vibrations (heat).
With the typical μM or less concentration of sample, the heat from radiationless decay is too small to affect the temperature of the solution.