The SwissFEL compact accelerator design is based on extremely low emittance electron beam from an RF photoinjector. Proper temporal and spatial shaping of the photocathode drive laser is employed to reduce the space charge emittance contribution. However, the ultimate limit for the beam quality is the thermal emittance, which depends on the excess energy of the emitted photoelectrons. By varying the photocathode laser wavelength it is possible to reduce the thermal emittance. For this purpose, we applied a tunable Ti:sapphire laser and an optical parametric amplifier which allow to scan the wavelength between 250 and 305 nm. The system permits to study the thermal emittance and the quantum efficiency evolution as function of the laser wavelength for the copper photocathode in the RF gun of the SwissFEL injector test facility. The results are presented and discussed.