The results of control possibility investigation for crucibleless AHP crystal growth method are considered. Numerical studies have been carried out basing on a specially designed global heat exchange model. The control methods based on radiation flux variation are considered. The changes of diaphragm opening in a diathermic cavity under a crystal and circular gap in the lateral thermal insulation against the melt surface have been found to change substantially the temperature fields and thermal fluxes at crystallization front due to the variations of radiation fluxes to the environment. The effect of the diaphragm height location and of diaphragm and surrounding constructions thermal-physical properties on the crystallization front shape have been considered.