Ammonia is produced in a reactor in which pseudoisothermal conditions can be approached by convective cooling of a reaction zone of the reactor by positioning at least a portion of the reaction zone in indirect contact with a flow of hot gas such as exhaust gas or preheated air. The hot gas may be supplied from a fired heater, a boiler, a reformer, a process air preheat furnace, a gas turbine, or the like. The reactor converts a feed stream of a purge gas or syngas to ammonia. The method may be implemented in a primary synthesis loop or in a purge gas loop of a new ammonia plant, or by retrofitting an existing ammonia plant. Cooperatively installed with a primary ammonia synthesis loop, the reactor increases total ammonia production.