Temperature-controlled polarization modulation near-field scanning optical microscopy measurements of a single supported L_{β^{'}} 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) lipid bilayer are presented. The effective retardance (S=2π(n_{e}-n_{o})t/λ, where t is the thickness of the bilayer and λ is the wavelength of light used) and the direction of the projection of the acyl chains (θ) were measured simultaneously. We demonstrate how one is able to align the system over the sample and measure a relative retardance ΔS, a crucial step in performing temperature-controlled experiments. Maps of ΔS and θ, with a lateral resolution on the order of ∼100 nm are presented, highlighting variations deriving from changes in the average molecular orientation across a lipid membrane at room temperature. A discussion of how this information can be used to map the average three-dimensional orientation of the molecules is presented. From ΔS and the known thickness of the membrane t the birefringence (n_{e}-n_{o}) of the bilayer was determined. Temperature-controlled measurements yielded a change of ΔS∼(3.8±0.3) mrad at the main transition temperature (T_{m}∼41^{∘}C) of a single planar bilayer of DPPC, where the membrane transitioned between the gel L_{β^{'}} to liquid disorder L_{α} state. The result agrees well with previous values of (n_{e}-n_{o}) in the L_{β^{'}} phase and translates to an assumed average acyl chain orientation relative to the membrane normal (〈ϕ〉∼32^{∘}) when T<T_{m} and 0^{∘} when T>T_{m}. Evidence of super heating and cooling are presented. A discussion on how the observed behavior as T_{m} is approached, could relate to the existence of varying microconfigurations within the lipid bilyer are presented. This conversation includes ideas from a Landau-Ginzburg picture of first-order phase transitions in nematic-to-isotropic systems.