Answer
Please see the work below.
Work Step by Step
We are given that the two objects absorb the same amount of heat, so $Q_1=Q_2$
$\implies m_1c_1\Delta T_1=m_2c_2\Delta T_2$
This equation can be rearranged as $\frac{\Delta T_1}{\Delta T_2}=\frac{m_2c_2}{m_1c_1}$.
The above equation shows us that the temperature difference depends on the mass and specific heat and it doesn't depend on the coefficient of expansion or thermal conductivity.
