Suggestions for Software to Model Temperature of a Zone Without HVAC?

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EnergyPlus can do this. You would define the solar oven as a zone, with its surface geometry and constructions, then not create any HVAC objects (thermostats, systems, etc.). To model a solar oven, be sure to get things like building orientation and weather file data correct.

When you install EnergyPlus, it comes with an ExampleFiles folder with lots of models (.idf files) to showcase various features. There is a 1ZoneUncontrolled.idf that would show how to define a zone without HVAC equipment.