The influence of the blackbody radiation field on the g factor of light hydrogenlike ions is considered within the framework of quantum electrodynamics at finite temperature for bound states. One-loop thermal corrections are examined for a wide range of temperatures. The numerical results for 1s, 2s, 2p1/2, and 2p3/2 states are presented. It is shown that for excited states, finite temperature corrections to the bound-electron g factor are close to the level of current experimental uncertainty even at room temperatures and can be discerned within the measurements anticipated in the near future.