The average normal body temperature measured in the mouth is 310 K. What would Celsius thermometers read for this temperature?

$\text{310K}$ would be ${37}^{\circ} \text{C}$
The Kelvin scale and Celsius scale are the same, so if the temperature increased by $\text{1K}$ then it also increases by ${1}^{\circ} \text{C}$.
The only difference between the two scales is that Kelvin starts at $\text{0K}$, which is equivalent to absolute zero or $- {273}^{\circ} \text{C}$.
Room temperature in Kelvin is about $\text{298K}$ $\left({25}^{\circ} \text{C}\right)$.