my dd2 won't have covers over her at night either - she will for first 5 inutes, but as soona s she is alseep they are off and if you recover her she wakes, so its not worth it. imo. we found that she kept cosier by using a fleece blanket instead of a sheet, helps with the nappies too!
Was going to suggest fleece blanket over the fitted sheet as well. I always did this for DS2 in his moses basket when newborn, and he was really snuggly (december baby and freezing cold in our room!) and it was bone dry for him even when his nappy leaked.