A test apparatus for evaluating thermal properties of a test specimen across a wide range of thermal conductivities and temperature ranges using a flat plate cup cryostat. The test apparatus includes: a heater assembly having an upper surface to receive a test specimen; a cold plate positioned on top of the test specimen; a vessel comprising an outer cylindrical tube closed on a bottom end by the cold plate; an inner cylindrical tube concentrically received in an upper portion of the outer cylindrical tube above the vessel to vent the vessel; insulation material surrounding at least the heater assembly, test specimen, cold plate, and vessel; a sensor that detects boiloff or evaporation rate of liquid from the vessel vented from the inner cylindrical tube; temperature sensors positioned to detect temperatures of the heater assembly and the cold plate; and a data recording device to record the boiloff or evaporation rates and temperature values.