We present modifications to conventional nanoindentation that realize variable temperature, flat punch indentation of ultrathin films. The technique provides generation of large strain, thin film extrusion of precise geometries that idealize the essential flows of nanoimprint lithography, and approximate constant area squeeze flow rheometry performed on thin, macroscopic soft matter samples. Punch radii as small as 185 nm have been realized in ten-to-one confinement ratio testing of 36 nm thick polymer films controllably squeezed in the melt state to a gap width of a few nanometers. Self-consistent, compressive stress versus strain measurements of a wide variety of mechanical testing conditions are provided by using a single die-sample system with temperatures ranging from 20 to 125 degrees C and loading rates spanning two decades. Low roughness, well aligned flat punch dies with large contact areas provide precise detection of soft surfaces with standard nanoindenter stiffness sensitivity. Independent heating and thermometry with heaters and thermocouples attached to the die and sample allow introduction of a novel directional heat flux measurement method to ensure isothermal contact conditions. This is a crucial requirement for interpreting the mechanical response in temperature sensitive soft matter systems. Instrumented imprint is a new nanomechanics material testing platform that enables measurements of polymer and soft matter properties during large strains in confined, thin film geometries and extends materials testing capabilities of nanoindentation into low modulus, low strength glassy, and viscoelastic materials.