The text mentions a 'heavenly world.' Is this the same as the typical idea of heaven?

No, the 'heavenly world' described in Chapter 37 is presented as a concept distinct from a traditional afterlife destination for sensual enjoyment. The text defines heaven as the Vairaj (the Cosmic Being) itself, a state of realizing the Cosmic Self-form which is free from mental grief. This divine heavenly state is characterized by the absence of disease, worry, sorrow, hunger, thirst, and the fear of old age or death. It is a state of fearlessness and non-duality. The chapter explicitly critiques the pursuit of a conventional heaven, calling it a mere place for sensual enjoyment and questioning its value if it lacks the remembrance of the Lord.