Definition of "cordially"

I may ask you, then, cordially to thank Sir George Goldie for all that he has done for the Society.

1893, Royal Geographical Society, The Geographical Journal, London

My dear Monsieur Durand,—I am sending you[....] / Ever most cordially yours, Iv. Tourguéneff.

1898, Ivan Sergeevich Turgenev, Tourguéneff and his French Circle

A rail tour on Sunday, March 12, in which non-members are cordially invited to participate, will leave St. Pancras at approximately 2 p.m. [...].

1961 February, “Society column: Branch Line Society”, in Trains Illustrated, page vii