Thai does not, at present, have A340s, although it has (subject to a disagreement over the price of shrimp!) five A340-5/600 on order. The -500s would be used for US flights and the -600s, for flights to Europe.
Thai's expansion plans are on ice at the moment, as it was intended that they would pay for the aircraft with shrimp. UAL, as desperate as they are, decided that $330m worth of shrimp, was not acceptable as a way of paying for seven of its -400s!