There is no apostrophe in Peoples Temple. There are references throughout newspaper articles, legal documents, correspondence and even some of the Temple’s own material – especially from its Indiana and early Redwood Valley days – to People’s Temple or, even more rarely, Peoples’ Temple, but the preferred spelling is “Peoples Temple.”
Similarly, while there are documents which indicate the contrary, the group was best known as Peoples Temple, without the article “the” preceding it. In its use as an adjective – “the Peoples Temple choir,” “the Peoples Temple philosophy,” “the Peoples Temple leadership” – the “the” is appropriate, but as a stand-alone name, the group’s name is simply “Peoples Temple”.
The play called “The People’s Temple” deliberately inserted the apostrophe to differentiate the drama from the group itself.