WHSG24301JM Gigabit LAN Transformer

Yes. The WHSG24301JM is rated -55 °C to +125 °C at the component, the widest range among the Gigabit parts here. Two things to settle first: it does not support PoE, so the port has to be powered locally; and -55 °C is the component's lower limit, not a demonstrated cold-start capability for the finished product. Whether a link comes up at low temperature depends on the PHY, the cable and the unit's thermal start-up, so it has to be measured in the target configuration.

To the common-mode termination network, not to a power rail: the TXCT and TDCT centre taps of the WHSG24301JM carry no DC balance current rating, and termination values should follow the reference design for the target PHY. PoE-rated alternatives are listed in the 10/100/1000 BASE-T range.

No. WHSG24301JM material in its original packaging is managed at +10 °C to +40 °C. The datasheet separates the powered operating range from the range that applies to packaged material in storage, and it is the packaged figure that governs warehousing. Warehousing and transit is where this most often goes wrong, because the wide operating range invites the assumption that boxed material can sit in a hot or freezing location.