a layer of muslin may work just fine- i've made quite a few lightweight (florida) quilts with muslin for batting- they came out very well-
cotton batting tends to be kind of heavy-
some people just use a layer of flannel for batting too- those work out nice also.
if you want batting i would go with a very low-loft lightweight one- ...but i don't know if those are ideal for tied quilts- the muslin or flannel would be fine for a tied quilt