Induction cores are used to accelerate heavy ion beam array, which are built around the outer diameter of the cryostat housing the superconducting quadruple array. Compact cryostat is highly desirable to reduce the cost of the induction cores. Recent experiences in fabrication of a cryostat for single beam transport revealed that it is possible to reduce the spacing in the cryostat vacuum jacket by using low-emissivity thermal insulation material instead of conventional MLI. However, it is labor-intensive to install the new type of insulation as compared with using MLI. It is promising to build a cost-effective compact cryostat for quadruple magnet array for heavy ion beam array transport by using low-emissivity material combined with conventional MLI as radiation insulation. A matrix of insulation designs and tests will be performed as the feasibility study and for the selection of the optimal thermal insulation as the Phase I work. The selected mixed insulation will be used to build prototype compact cryostats in the Phase II project, which are aiming for housing quadruple doublet array. In this STTR phase I study, a small cryostat has been designed and built to perform calorimetric characterization of the heat load in a liquid helium vessel insulated with a vacuum layer with a nominal clearance of 3.5 mm.