Dimensional formula of Heat(Q) = M(^1)L(^2)T(^-2)
Dimensional formula of Specific Heat Capacity = M(^0)L(^2)T(^-2)K(^-1)
The heat capacity is defined as
[tex]\displaystyle \lim_{\Delta T \to 0}\dfrac{\Delta Q}{\Delta T}[/tex]
So, in particular, it is the ratio of heat and temperature, and therefore its dimension is J/K, i.e. Joule per Kelvin.