This can be done with the following CSS code (that just needs to be added to the “Custom CSS” textarea in the “Plugin Options”):

.tablepress thead th,
.tablepress tfoot th {
	background-color: #ff0000;
}

To also change the hover color when sorting, and the background color of the column that is currently sorted, add

.tablepress thead .sorting_asc,
.tablepress thead .sorting_desc,
.tablepress thead .sorting:hover {
	background-color: #00ff00;
}