A thesis statement usually only iterates one point, allowing the essay to focus on explanation and support. For a three-point thesis statement, you should find three points that, together, support a single solid statement or idea; in other words, your thesis will still seem to contain a "single point," but also contains three main ideas that support that initial point. Additionally, for a shorter essay, the points need to be easy to explain in one paragraph each.
For Ray Bradbury's short story "There Will Come Soft Rains," most of the focus is on the humanization of technology compared to the actual needs of a human family, and how that technology remains "alive" years after the humans have died. One good thesis statement might be: "Although technology makes life easier, it only performs the tasks set by an intelligent mind, and without that purpose defined by intelligence, technology serves little purpose." This thesis concerns the use of technology, the limitations of decision making, and the need for technology to serve a "higher purpose," in this case, humanity.
Another thesis might contrast the technology used to make life easier -- the house -- with the technology that destroyed its inhabitants. You might write: "Although the automated house is a marvel of modern technology, it is useless in the face of a far simpler technology: fire." This thesis concerns the innovation required to create a house that automatically performs so many functions, and yet could not protect its inhabitants from the nuclear war, or itself from a simple kitchen fire. Again, there are three major points, each of which can be explained in a paragraph.
Another option is to make your thesis statement and then point out the three-point explanation you will use in your essay. For example: "Here is my thesis statement. This thesis is supported by Point A, Point B, and Point C." That will allow you more length to explain your points.