Hawking effect from dynamical spherical Vaidya black hole, Vaidya-Bonner black hole, and Vaidya-de Sitter black hole is investigated using the improved Damour-Ruffini method. After the new tortoise coordinate transformation in which the position 𝑟 of event horizon is an undetermined function and the temperature parameter 𝜅 is an undetermined constant, the Klein-Gordon equation can be written as the standard form at the event horizon, and both 𝑟 and 𝜅 can be determined automatically. Then extending the outgoing wave from outside to inside of the horizon analytically, the Hawking temperature can also be obtained automatically.