Does the measured temperature of a body depends on the specific heat capacity of the material inside the thermometer we are using? Since the rise of temperature in a body is measured by its specific heat capacity, will my measurement of a body's temperature changes if i use a different thermometer rather than the usual mercury thermometer
 A: 
Since the rise of temperature in a body is measured by its specific
heat capacity

That is incorrect.
Suppose we have a very large heat source, at a constant temperature $T_{\infty}$. Now we insert a much smaller object, at a different temperature, say $T_0$.
The Laws of Thermodynamics state that given enough time the temperature of the smaller body will become equal to the temperature of the large heat source.
This outcome in no way depends on the heat capacity of either body or other factors. Heat capacity, mass and other factors can influence greatly the rate at which the smaller object tends to $T_{\infty}$ (see e.g. Newton's Law of Cooling), but not the final temperature.
This is true also if both objects are of more comparable sizes and of different temperatures, say $T_1$ and $T_2$. Given enough time, both will exchange heat, heat flowing from hot to cold, until they both reach the same end temperature $T_e$, where:
$$T_1<T_e<T_2$$
(assuming $T_2>T_1$)
A: No, It depends up on the scale you are using to measure the temperature.
With different material inside thermometer, the shown temperature will depend on the calibration of the scale with respect to that material
