The very bright electron beam required for an x-ray free-electron laser (FEL), such as the Linac Coherent Light Source (LCLS), is susceptible to a microbunching instability in the magnetic bunch compressors, prior to the FEL undulator. The uncorrelated electron energy spread in the LCLS can be increased by an order of magnitude to provide strong Landau damping against the instability without degrading the FEL performance. To this end, a `laser-heater' system has been installed in the LCLS injector, which modulates the energy of a 135-MeV electron bunch with an IR laser beam in a short undulator, enclosed within a four-dipole chicane. In this paper, we report detailed measurements of laser heater-induced energy spread, including the unexpected self-heating phenomenon when the laser energy is very low. We discuss the suppression of the microbunching instability with the laser heater and its impact on the x-ray FEL performance. We also present the analysis of these experimental results and develop a three-dimensional longitudinal space charge model to explain the self-heating effect. Show Partial Abstract