We present a thermal model of the nucleus of comet 46P/Wirtanen, constrained by the temporal variations of the water production rate, in order to understand the activity on its surface. We consider a spherical nucleus with a macroscopic mosaic of small and numerous active and inactive regions. At heliocentric distances r(h) > 1.5 AU, the active regions represent 5-15% of the surface. At similar to1.5 AU, a rapid increase takes place and the active fraction reaches 70 to 100% in about 10 days, and then remains approximately constant up to perihelion where Q(H2O) = 1.3 +/- 0.3 x 10(28) molecule s(-1). Post-perihelion, this fraction returns to similar to10%. The model is consistent with a geometric albedo less than or equal to0.06. A refractory crust likely forms post-perihelion and can explain the variations of the activity over an orbit. Finally, we derived an erosion of similar to0.5 m per revolution and a remaining lifetime for the nucleus of several hundred revolutions.