We investigate nuclear pasta phases appearing in hot neutron-star matter based on the compressible liquid-drop model, where the matter consists of a dense liquid phase and a dilute gas phase separated by a sharp interface. The surface tension is calculated self-consistently from the Thomas–Fermi approximation, and it depends on temperature and isospin asymmetry. We employ relativistic mean-field (RMF) models with different symmetry energy slopes to describe nuclear interactions. It is found that the RMF models with smaller symmetry energy slopes result in various pasta phases at low temperatures, whereas those with larger symmetry energy slopes yield only the droplet configuration up to the crust-core transition density. We examine the occurrence and influence of pasta phases in proto-neutron stars with a constant entropy per baryon. These pasta phases may occur in the inner crust and play an important role in the thermal evolution of the star.