The purpose of this paper is to analyze the variation in the line width with height in the inner corona (region above 1.1 Rsun), by using the spectral data from LASCO-C1 aboard SOHO. We used data acquired at activity minimum (August - October 1996) and during the ascending phase of the solar cycle (March 1998). Series of images acquired at different wavelengths across the Fe X 637.6 nm (red) and Fe XIV 530.3 nm (green) coronal lines by LASCO-C1 allowed us to build radiance and width maps of the off-limb solar corona. In 1996, the line width of Fe XIV was roughly constant or increased with height up to around 1.3 Rsun and then it decreased. The Fe X line width increased with height up to the point where the spectra were too noisy to allow line width measurements (around 1.3 Rsun). Fe X showed higher effective temperatures as compared with Fe XIV. In 1998 the line width of Fe XIV was roughly constant with height above the limb (no Fe X data available).