The character you see in your display program depends on whatever font or character set it uses. Different character sets use different codes for the degree symbol. Many character sets don't include any degree symbol at all.
Try changing HyperTerminal's display font to Fixedsys (click View - Font), and then send character 248.
Most Hyperterminal fonts are using Windows (ANSI) char set, but the default Terminal font uses DOS/OEM char set. It also has a ° character, but with different coding.