The coupled Stokes and heat conduction equations \(\frac{\partial u_{i}}{\partial t}= -\frac{\partial p}{\partial x_{i}}+\Delta u_{i}+g_{i}T\), \(\frac{\partial u_{i}}{\partial x_{i}}=0\), \(\frac{\partial T}{ \partial t}+u_{i}\frac{\partial T}{\partial x_{i}}= \Delta T\) are considered with appropriate initial and boundary conditions. The authors study the continuous dependence of solution on spatial geometry, and derive an error estimate for the difference between the exact solution to the true physical problem \(( u,T,p)\) and the exact solution on an approximate domain. The derivation involves the introduction of various auxiliary problems and estimates in \(L^{p}\) for related functions.