Answer
It depends on the different scale thermometer from which sample's temperature was measured.
If the temperature is measured by Celsius scale thermometer then sample's new temperature will be $20^{\circ}c$.
If the temperature is measured by Fahrenheit scale thermometer then sample's new temperature will be $37.78^{\circ}c$ .
If the temperature is measured from kelvin scale thermometer then sample's new temperature will be $275^{\circ}c$.
Work Step by Step
The conversion of different scale of temperature given as $$\frac{C}{100}=\frac{F-32}{180}=\frac{K-273}{100}$$where C is temperature in Celsius scale and F is temperature in Fahrenheit scale and K is temperature in Kelvin scale.
The new temperature of sample's after doubled the temperature will vary as measuring from different scale thermometer.
1.On measuring the temperature from Celsius scale thermometer:
Initial temperature $= 10^{\circ}C$
After doubled the temperature the new temperature becomes $20^{\circ}C$.
2.On measuring the temperature from Fahrenheit scale thermometer:
Initial temperature $= 10^{\circ}C=50^{\circ}F$
After doubled the temperature the new temperature becomes $100^{\circ}F=100(\frac{100-32}{180}) =37.78^{\circ}C$
3.On measuring the temperature from Kelvin scale thermometer:
Initial temperature $=10^{\circ}C=274K$
After doubled the temperature the new temperature of sample's becomes 548K$=(548-273)^{\circ}C=275^{\circ}C$
