A fitted bottom sheet is formed with opposing pockets adapted to receive the head end and foot end of a mattress or cot. A top covering assembly including a top covering, a heat-reflecting sheet, and a top sheet attaches securely to the foot end of the fitted bottom sheet. The top covering assembly and fitted bottom sheet may be installed simultaneously as an integral unit on a cot or mattress. The top covering assembly may be formed with a pocket for receiving additional thermal insulation such as another blanket. Embodiments may be securely and neatly placed on rectangular mattresses, nonrectangular mattresses, and bedding without mattresses such as folding camp cots.