A spectral method is developed based on the primitive variables for the time-dependent solution of the flow and the temperature past a spherical droplet. Both Chebyshev and Legendre polynomials are used to expand the velocity, pressure, and temperature in the radial and angular directions, respectively. The fractional time-stepping method suggested by Orszag (Orszag et al., 1980) is used for solving the flow and the pressure fields. Euler backward differencing is used for the integration of the energy equation. The computed steady-state drag coefficients are compared to those found in the literature for Reynolds numbers in the range from 0.5 to 50 for both the continuous and the dispersed phase. The transient drag coefficients and Nusselt numbers are compared with our previous study using a stream function-vorticity formulation (Nguyen et al, 1993). The comparison indicates that the present model is capable of predicting the correct nature of the flow and heat transfer associated with a droplet.