Time-dependent photodetachment action spectra for the linear hydrocarbon anions C4H- and C6H- are investigated using the cryogenic Double ElectroStatic Ion Ring ExpEriment. The radiative cooling characteristics of these ions on the millisecond to seconds timescale are characterized by monitoring changes in their spectra as the ions cool by spontaneous infrared (IR) emission. The average cooling rates, extracted using Non-negative Matrix Factorization, are fit with 1/e lifetimes of 19 ± 2 and 3.0 ± 0.2 s for C4H- and C6H-, respectively. The cooling rates are successfully reproduced using a simple harmonic cascade model of IR emission. The ultraslow radiative cooling dynamics determined in this work provide important data for understanding the thermal cooling properties of linear hydrocarbon anions and for refining models of the formation and destruction mechanisms of these anions in astrochemical environments.