The most common method to characterize electronic components at low temperatures are measurements through cryogenic probe stations. The systems combine up to six individually movable measuring tips with a cryostat. When more than 6 contacts are required, you can use a Multi-Contact Wedge (MCW). An MCW is a wedge-shaped setup of a dozen or more measuring tips which are used instead of a single contact.  A probe station can fit up to 6 MCWs. This facilitates more than enough contact points for any standard application. The setup is limited by the heat load because many feedthroughs lead to an increase in heat input. This can be avoided by choosing a probe station with a low base temperature.
Lake Shore is the market leader for cryogenic probe stations. Multi-Contact Wedges can be used in all Lake Shore systems. GGB Industries, specialized in the manufacturing of measurements tips, provide customized MCWs.  

• Temperature range: 2 K - 675 K
• Number of flexible probe pins: up to 6
• Magnetic field: up to 2.5 T

More about cryogenic probe stations