The scalability of quantum computing systems is constrained by the wiring complexity and thermal load introduced by dense wiring for control, readout and synchronization at cryogenic temperatures. To address this challenge, we explore the feasibility of wireless communication within a cryostat for a multi-core quantum computer, focusing on wireless channel characterization at cryogenic temperatures. We propose to place on-chip differential dipole antennas within the cryostat, designed to operate at 28 GHz in temperatures as low as 4 K. We model the antennas inside a realistic cryostat and, using full-wave electromagnetic simulations, we analyze impedance matching, spatial field distribution, and energy reverberation due to metallic structures. The wireless channel is characterized through measured channel impulse response (CIR) across multiple receiver antenna positions. The results demonstrate potential for reliable shortrange communication with high Signal-to-Noise Ratio (SNR) and limited sensitivity to positional variation, at the cost of nonnegligible delay spread, due to significant multipath effects.