The open set recognition (OSR) problem aims to identify test samples from novel semantic classes that are not part of the training classes, a task that is crucial in many practical scenarios. However, the existing OSR methods use a constant scaling factor (the temperature) to the logits before applying a loss function, which hinders the model from exploring both ends of the spectrum in representation learning -- from instance-level to class-specific features. In this paper, we address this problem by enabling temperature-modulated representation learning using a set of proposed temperature schedules, including our novel negative cosine schedule. Our temperature schedules allow the model to form a coarse decision boundary at the beginning of training by focusing on fewer neighbors, and gradually prioritizing more neighbors to smooth out the rough edges. This gradual task switching leads to a richer and more generalizable representation space. While other OSR methods benefit by including regularization or auxiliary negative samples, such as with mix-up, thereby adding a significant computational overhead, our schedules can be folded into any existing OSR loss function with no overhead. We implement the novel schedule on top of a number of baselines, using cross-entropy, contrastive and the ARPL loss functions and find that it boosts both the OSR and the closed set performance in most cases, especially on the tougher semantic shift benchmarks.