they sleep in all kinds of positions, i have laughed so many times at my chicks. what is even funnier is they will be up moving around and then boom they are flat on their side sound a sleep. it looks like they faint.
as far as the temp here is something from mypetchicken that may help.. you may want to put something across the top of the brooder to hold in heat.
Baby chicks need to be kept pretty hot. Think sauna! The first week of their lives they require an air temperature of 95 degrees, the second week 90 degrees, and so on - going down by 5 degrees per week until they're ready to transition to "outside". A 250-watt infrared heat lamp is the best way to achieve this, placed right in the middle of their living area and suspended off the ground. The height of the light will depend on what it takes to achieve your target temperature.
We recommend a red heat bulb for a few reasons: one, with a bright white light constantly glaring it can be hard for them to sleep. The red light is darker and provides them some respite. Two, red lights help prevent them from pecking one another.