Dielectric relaxation is studied in 10 nm HfO2 thin films which are deposited by atomic layer deposition on TiN and Pt electrodes. Transient currents are recorded from 10-3 s to 10 s, as a function of bias (0.1 V to 1 V) and temperature (20 °C to 180 °C). A Curie-von Schweidler law is observed, I = Q0/tα. The power law exponent α is constant with bias and strongly depends on the temperature (varying in the 0.65–1.05 range, with a peak at 75 °C). The amplitude Q0 is described by a relation of the form Q0 = C0Vβ, where the factor C0 is weakly activated and the exponent β varies with temperature (in the 0.9–1.5 range as T varies). Transient currents are discussed along with tunneling based models from the literature. To complement transient current experiments, admittance spectroscopy (conductance G and capacitance C) is performed at low frequencies, from 0.01 Hz to 10 kHz. The dispersion law of the conductance is of the form G ∼ ωs. The capacitance is the sum of two terms, a non-dispersive term (C∞) and a low-frequency dispersive term, CLF ∼ ω-n. The critical exponents s and n verify s ≈ α and n ≈ 1-α. At room temperature, the dielectric constant is expressed as ɛ′ = Δɛ′ f-n+ ɛ′∞, where ɛ′∞ = 11.1, n ≈ 0.2/0.3 (Pt/TiN), and Δɛ′ ≈ 1.5/0.7 (Pt/TiN).