The paper discusses the possibility of building semiconductor lasers whose wavelength stays nearly constant with ambient temperature variation. Several factors affecting the lasing wavelength change with temperature variation in both distributed feedback lasers and Fabry-Perot lasers are addressed and the optimum design of bandgap temperature dependence for the active layer material is discussed. It is pointed out that the most important challenge we face in building temperature-insensitive wavelength lasers is the development of a temperature-insensitive bandgap material for the active layer. Based on published data, it is speculated that such a laser could be developed using a Hg1-xCdxTe/CdTe double heterostructure. Although no data is available yet, we expect a Ga1-xInxAs1-yBiy III-V alloy semiconductor can be used for this purpose. Recently reported T1xIn1-x-yGayP III-V alloy semiconductor might be another promising candidate. Such lasers will greatly advance applications of WDM (Wavelength-Division-Multiplexing) technology to optical fiber communication systems and contribute to network innovations.