If a daycare center affiliated with a Temple and located within the Temple (with its own entrance)requires painting of classroom walls and a non-Jewish painter is hired for the job, is it acceptable to allow them to paint on Shabbat?

A non Jew may not work in property owned by a Jew on Shabbat, even if it is for the non Jew's convenience. (see Shulchan Aruch Orach Chaim ch. 244 for details)