An antiferromagnetic domain wall in a thermal gradient is found to experience a force towards colder regions upon the application of a uniform magnetic field along the easy axis. This force increases with the strength of the applied field and, for sufficiently high values, it overcomes the entropic force the that pushes wall towards the hotter regions. The force is proportional to the thermal gradient and it shows a linear dependence with the net magnetic moment of the domain wall induced by the field. The origin of this force lies on the increase of the domain wall reflectivity due the field-induced sizable break of antiferromagnetic order inside it, which turns it into an efficient barrier for magnons, which transfer linear momentum to the domain wall when they are reflected on it
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