Answer
If both objects have the same specific heat, the less massive one will experience greater $\Delta T$.
If they have the same mass, the one with the lesser specific heat will experience a greater $\Delta T$.
Work Step by Step
From the equation for specific heat,
$c=\displaystyle \frac{Q}{m\Delta T}$, we express $\displaystyle \Delta T=\frac{Q}{mc}.$
With Q being constant, the temperature difference depends on the term $mc.$
So,
if both objects have the same specific heat,
the less massive one will experience a greater $\Delta T$.
If they have the same mass, the one with the lesser specific heat will experience a greater $\Delta T$.
