We study about an approximation method of the Hawking radiation. We analyze an massless scalar field in exotic black hole backgrounds models which have peculiar properties in black hole thermodynamics (monopole black hole in SO(3) Einstein-Yang-Mills-Higgs system and dilatoic black hole in Einstein-Maxwell-dilaton system). A scalar field is assumed not to be couple to matter fields consisting of a black hole background. Except for extreme black holes, we can well approximate the Hawking radiaition by 'black body' one with Hawking temperature estimated at a radius of a critical impact parameter. [4][5][6][7][8][9][10], it has been less investigated because many of them are only obtained numerically that it takes much works compared with ones of analytically obtained. But we need to investigate for many reasons. Particularly, a monopole black hole which was found in SO(3) Einstein-Yang-Mill-Higgs (EYMH) system [11][12][13][14] is important because it is one of the counterexample of the black hole no hair conjecture [15]. Moreover, if we consider the evaporation process of the Reissner-Nortström (RN) black hole, it may become a monopole black hole and the final product (a regular gravitating monopole) could be a good candidate for the remnant of the Hawking radiation in such a system.From such view points, we study an approximation method of the Hawking radiation which may reduce our labor and discuss its validity in this paper. Throughout this paper we use units c =h = 1. Notations and definitions as such as Christoffel symbols and curvature follow Misner-Thorne-Wheeler [16].We consider two models in which black hole solutions have peculiar properties in black hole thermodynamics.(I) The SO(3) EYMH model as * electronic mail:tamaki@gravity.phys.waseda.ac.jp † electronic mail:maeda@gravity.phys.waseda.ac.jpwhere κ 2 ≡ 8πG with G being Newton's gravitational constant. L m is the Lagrangian density of the matter fields which are written asF a µν is the field strength of the SU(2) YM field and expressed by its potential A a µ aswith a gauge coupling constant e. Φ a is a real triplet Higgs field and D µ is the covariant derivative:The parameters v and λ are the vacuum expectation value and a self-coupling constant of the Higgs field, respectively.(II) The Einstein-Maxwell-dilaton (EMD) model aswhere φ and F are a dilaton field and U(1) gauge field, respectively. For black hole solutions, we assume that a space-time is static and spherically symmetric, in which case the metric is written aswhere f (r) = 1 − 2Gm(r)/r. We consider spacetime, which have a regular horizon and is asymptotically flat. In such a background spacetime, we consider a neutral and massless scalar field which does not couple to the matter fields such as the YM field or the Higgs field. The eq. of motion is described by the Klein-Gordon equation as Φ ;µ ,µ = 0.This equation is separable, and we should only solve the radial equation 1