Dynamic heterogeneity refers to the presence of spatially variable local dynamics. In blends of miscible polymers, this heterogeneity can arise from differences in segmental dynamics. Its origins in polymer blends have been attributed to both local effects (self-concentration, caging) and long-ranged effects (concentration fluctuation), but its length scales are not fully understood. The atomic-level resolution required to characterize dynamic heterogeneity poses challenges for purely experimental approaches. As a result, we use molecular dynamics simulations to study how the length scales of dynamic heterogeneity vary with temperature and blend composition in blends of polyethylene oxide (PEO) and polymethyl methacrylate (PMMA). Using a combination of local and collective dynamics analyses based on local fluctuations and Rouse modes, we find that the length scales of dynamic heterogeneity are asymmetric for PEO and PMMA. Blending causes stronger reductions in local polymer dynamics than enhancements for both species. Deviations in local dynamics from pure system dynamics are suggested to be caused by composition dependent packing structures that arise due to the presence of side chains on PMMA and lack of side chains on PEO. Blending also alters the collective dynamics for both species at all tested chain lengths. However, it has a notably stronger effect on PEO chains with at most 10 monomers and PMMA chains with at least 5 monomers. These results provide fundamental insights into how dynamic heterogeneity arises in multi-component systems due to blending and open questions about the generalization of these asymmetrical behaviors to other systems and tunability of the length scale of dynamic heterogeneity using temperature and blend composition.