We have developed a small purely electrostatic ion-beam trap which may be operated in thermal equilibrium at precisely controlled temperatures down to 10 K. Thus, we avoid magnetic field induced mixing of quantum states and may effectively eliminate any influence from absorption of photons from blackbody radiation. We report the first correction-free measurement of the lifetime of the 1s2s2p {4}P{5/2}{0} level of 4He(-) yielding the high-precision result 359.0 +/- 0.7 micros. This result is an essential proof-of-principle for cryogenic electrostatic storage rings and traps for atomic and molecular physics.