While reading paper Constitutionalism and Elections in Thailand by Clark D. Neher, found in the book Modern Thai politics I have found that the one-to-three-seats constituencies weren't the only system used in the past.
The Senate did accede to the governments request that the province be made the electoral constituency and the number of representatives from each province be based on the population within the constituency. The alternative proposal, narrowly defeated by the Senate, had called for single-member district constituencies.The election was held on February 10 1969, ending more than 10 years of military dictatorship without any parliamentary control, however in fact the winner of the election was the previous dictator Field Marshal Thanom Kittikachorn. Also, the legislature did not reach the end of its term, as in 1971 Thanom staged a coup against his own government and dissolved the parliament again.
The Senate's support for the provincial constituencies was due certainly to the government's intimation that the elections themselves might be cancelled if its wishes in that matter were not heeded. The pressure on senators to support provincial constituencies reflected the party's power among provincial urban politicians who had far less hope of winning elections in rural single-member district constituencies.