setAxisScale(QwtPlot::xBottom, fromValue, toValue);
setAxisTitle(QwtPlot::xBottom, "my axis title");

fromValue and toValue represent the min and max of my xScale (in x values, not pixels).
Indeed, I manipulate the x and y scales myself to be able to draw multiple curves which have different scales. Next, I can change the axis scale (only the Y one as all my curve have the same time base) according to the selected curve.