Hi you can grow tomatoes indoors. If you google 'growing tomatoes indoors' many ideas will pop up.

Go ahead an start some plants (I'd start with a handful of seedlings). You may lose some or find others grow better. Keep the strong growing plants.

Your temperature sounds good. Wood heat can be very drying - if you can get your hands on potting soil for hanging plants (they have the moisture retention formula) it would help a great deal.

I learn gardening by doing. I've grown all sorts of plants indoors at various locations I have lived - light is a major factor for plants producing flowers, fruit etc.

Go on and give it a try. I'm going to get some going myself this week too.

Happy New Year,
Peggy