This is confused.
Space is not magically cold. It's just a vacuum. Also, heat does not travel through space. You are correct that infra-red travels through space, but infra red is not heat. Normally that distinction isn't terribly important, but in this context it is.
In space heat is caused by infrared light striking an object. Infrared is easily converted to heat. But because you're in a vacuum, there is no heat carried by conduction or convection. On earth the most of the radiation doesn't make it to the ground. That's one of the wonderful things about our atmosphere. But if you were unprotected on the light side of the shuttle, you'd fry. WHen the infra-red from the sun struck your body, it would turn to heat. But because you are in a vacuum, your body has no way to get rid of the heat except via radiation. It turns out that while our bodies just aren't very good at creating the right sort of radiation. We do create some, but in normal situations most of our heat loss is due to convection and evaporation. So on the light side of the shuttle, you'd be taking in far more heat that you were giving off. Eventually you'd boil over, literally.
On the dark side of the shuttle there is the opposite problem. Your body is no longer taking in any radiation, so there's no source of heat. On earth, even in a completely dark spot, you can get heat by contact with the air and with objects. Also, the atmosphere distributes the sun's radiation so that even in a shadow you're getting some radiation. But on the dark side of the shuttle, you get no radiation, and you get no warmth via conduction or convection either. However, your body does continue to produce radiation. Since your body is losing heat via radiation, but not gaining any, your body will slowly cool until it reaches nearly absolute zero.
Were it not for the pressure problems, you'd last a lot longer on the dark side of the shuttle in your skivvies than you would in a vat of dry ice. This is because in space your only heat loss is through radiation. In dry ice you continue to lose heat via radiation, but you also lose it via conduction and convection. So you'll freeze faster in dry ice than in space. As far as heat loss goes, all you need is space is a thin foil suit that is extremely reflective on both sides.