```python
"""Melt a row of ice one simultaneous step at a time."""

def thaw_row(row: str, steps: int) -> str:
    if not isinstance(row, str) or not row:
        raise ValueError("thaw_row expects a non-empty string row")
    
    if not (isinstance(steps, int) and steps >= 0):
        raise ValueError("steps must be a non-negative integer")
    
    rows = [row]
    
    for _ in range(steps):
        new_rows = []
        for r in rows:
            new_row = ""
            for i, cell in enumerate(r):
                if i == 0 or i == len(r) - 1 or (i > 0 and r[i - 1] == ".") or (i < len(r) - 1 and r[i + 1] == "."):
                    new_row += "."
                else:
                    new_row += "#"
            new_rows.append(new_row)
        rows = new_rows
    
    return rows[-1]
```