Since the very first demonstration of a vertical-cavity surface-emitting laser (VCSEL) incorporating subwavelength high refractive index contrast grating (HCG) membrane mirror in 2007 by the group of Prof. Chang-Hasnain, numerous research groups around the world have presented devices based on the same concept emitting at wavelengths from ~400 to 1550 nm manufactured in gallium nitride (GaN), gallium arsenide (GaAs) and indium phosphide (InP) material systems. On one hand, an open access to a VCSEL cavity through an air gap combined with a very low inertia of an HCG mirror opened a way for a large range of emission wavelengths in MEMS tunable VCSELs. On the other hand, an air gap in a cavity generally hinders heat and current flow, while the potentially rather fragile HCG membrane is prone to mechanical instability. We present electrically-injected VCSELs incorporating monolithic HCG (MHCG) mirrors. An MHCG mirror being a special case of an HCG mirror, keeps the extraordinary features of an HCG such as scalability with wavelength, ultra-low thickness and very large power reflectance, but doesn't have to be surrounded by a low refractive index material and hence can be monolithically integrated with an all-semiconductor VCSEL cavity. We present an extensive analysis of the impact of the MHCG parameters on the modal properties and thermal stability of single- and double-mode devices, with various oxide apertures. We additionally compare MHCG VCSELs and generic distributed Bragg reflector VCSELs in terms of modal properties and temperature stability based on measured data and the results of computer simulations.