No, even if you only had one unit for a physical quantity, you would still need to specify that unit to know which physical quantity you are describing. E.g. “That object over there is 15” vs “That object over there is 15 kg”.
The symbol for temperature, measured in Celsius, is “°C”. It’s atomic and can’t be separated, since that would result in °, which represents the angle of something, not the temperature, and C, which is the symbol for Coulomb, which measures electric charge.