I've encountered this situation a few times lately and the things that have helped us so far are to nurse sidelying and with our bodies a little bit apart. If we are touching skin to skin I put a thin cloth between us because I hate that sweaty skin to skin feeling and I think it keeps ds awake too. Our bed is under a fan, so with the fan on, baby in just a diaper, not being too cuddled up together and a really light blanket or cloth (we use the A&A swaddles) it keeps us pretty cool for nursing down for a nap.
Try to keep the room as cool as possible during the day. Keep your blinds/coverings/whatever down or closed. If it would be cooler in your situation keep the windows closed to keep hot sun out(if this applies). Keep the door closed.
Our bedroom is warm, even if we do use the A/C. I have an overhead fan and box fan that really help even though it does increase electricty(but not as much as the A/C). A cool bath for DD helps too. Sometimes I take off most of my clothes when we nurse. Side-lying is also less body contact for us.