The thermal conductivity K(T) of polycrystalline YBa2(Cu1-xNx)3O7 with N=Zn and Al (0 less-than-or-equal-to x less-than-or-equal-to 0.1) and Y1-yMyBa2Cu3O7 with M = Pr and Gd (0 less-than-or-equal-to y less-than-or-equal-to 1.0) has been measured for temperatures 1.2 less-than-or-equal-to T less-than-or-equal-to 200 K. In the undoped samples, K(T) decreases slightly with decreasing temperature above T(c), with a strong enhancement of K(T) below T(c) reaching a maximum at approximately 50 K followed by a sharp decrease. Doping with Zn and Pr, which have been shown to dramatically disturb the superconductivity, rapidly depresses the maximum in K(T) even at concentrations that remain superconducting. This effect is not as dramatic for Al- and Gd-doped samples, which do not strongly depress the superconductivity. These data are discussed considering both phonon and electron thermal conduction mechanisms, and are compared with relevant theories, such as a modified BRT theory of phonon conduction within the superconducting state.