The temperature rising a little can cause them to keep spawning. Is the tank temp perhaps fluctuating when you have the house heating on?
If the female is getting exhausted it might be best to separate them until the season is over. Check the males for breeding tubercles, little white dots on gills and pectoral fins - when they go it's over for a while.
If you don't have space for the babies it may be hard to rehome them to decent long-term home so sadly the best thing to do is to not try to save them.