A nanoscale dynamic mechanical analysis (nano-DMA) measurement method has been successfully developed for use in evaluating nanoscale dynamic viscoelastic properties in small-scale polymer materials over a range of non-ambient temperatures from -120 oC to 500 oC. Measurements have been obtained with a nanoindentation measurement system, in which two key techniques are applied. One is a thermal protection system for control and prevention of thermal drift and noise. The other is an environmental control system for preventing corrosion at high temperatures and dew condensation at low temperatures. Measurement reliability was examined by using a combination of a thermal-mechanically stable fused silica and a homogeneous sample of isotropic polyethylene terephthalate (PET). Constant hardness and modulus values of the fused silica from -120 oC to 500 oC indicated that the measurements were not affected by thermal load drift and noise even at elevated temperatures. The PET sample exhibited no significant difference in temperature dispersions of storage elastic modulus, loss elastic modulus and loss tangent between the nanoindentation measurement data and bulk data measured with a conventional DMA method. A practical application involving surface-deteriorated polyethylene (PE) tubes was used to demonstrate the validity and usefulness of this nano-DMA method. Infrared spectroscopic imaging revealed that the surface layer of the PE tubes was oxidized to form a carbonylated (O=C<) layer. The storage elastic modulus and glass-transition temperature of the surface layer were much higher than the corresponding values of the interior. These data indicate a plausible reason for why the PE tube surface deteriorates to form brittle cracks.