Where to buy a heating blanket in Prati (Rome)

Tough one. I thought perhaps a COIN home store but it is quite far away from you. Maybe browse along Via Cola di Rienzo? Check the street market stalls that have household goods. There are (were when I lived there) many along Via Ottaviano near the Metro station.

Ask your landlord/hotel?

Do you mean a blanket or a heating pad? Either way, ask your landlord/front desk.

Or just buy a hot-water bottle.
I've bought two in Italy when I was cold, and generally the pharmacies sell them.