Answer
No such temperature exists.
Work Step by Step
A $1^{o}C$ difference in temeperature equals 1 K. The Kelvin scale starts at absolute zero, where the Celsius scale reads $-273.15^{o}C.$ So, for temperature expressed as T kelvins and $T_{C}$ degrees Celsius, the difference is constant
$T-T_{\mathrm{C}}=273.15$
No such temperature where $T=T_{C}$ exists.
The reason that there is a common temperature in the Fahrenheit and Celsius scales is that a one degree difference in temperature is not the same in these two scales.
For example, from freezing to boiling points of water at normal atmospheric pressure, there are 100 degrees on the Celsius scale, while there are 180 in the Fahrenheit scale.
