How to squeeze text into a shape

• Save your work. Experiment first :-)
• Path Menu > Object to path - Convert the text to a path
• Path Menu > Path Effect Editor - Shows path effect editor at right
• Choose Envelope Deformation from drop down
• Click the Add button
• Select the Top bend path option (edit on canvas button - the left of the four btns on each row)
• Shift-drag out the tangents from the left and right node
• Repeat for the bottom bend
• For the left and right bends - optionally just move the upper and lower nodes closer together to pinch the left and right tips, but enure they stay vertically aligned

TIP - if you don't want the text to go right into the tips of the corners, add a '+' to the beginning and the end of the text and then when you're done, paint these characters white or transparent. This is because when you convert text to a path, it will ignore any leading or terminating spaces because they're not part of the 'path'

EDIT - additional example