My 60 year old t-80 thermostat (for furnace only, no a/c) is not working and I can't seem to find a replacement. Is there a new type of thermostat that's used to replace the t-80?

You won't, extinct many years ago. Is it heat only or Heat and AC? Just go to Home Depot or Lowe's and they can cross reference it. I don't have anything that old referenced.

Yep, HD has plenty for low cost Selecting the Right Thermostat for Your Home at The Home Depot (http://www.homedepot.com/c/selecting_right_thermostat_for_your_home_HT_BG_EL)