One idea would be to reduce the data to the cross-sectional dimension by running your analysis based on time-series averages. This is what statisticians refer to as the between estimator. For instance, if you want to find out what drives cross-sectional differences between your n individuals you could run a regression of the following type:
$$
\bar{y_i}=\alpha+\beta \bar{x_{i}}+e_i
$$
where $\bar{y_i}$ is the time series average of variable y of individual i and $\bar{x_i}$ is the respective time-series mean of variable x.
By taking time-series means you "remove" the time-series variation. I guess, to talk about variation rather than variance is to be preferred in this context.