Just watch your ambient temps there Debbie, okay? As long as your indoor temps are warm, like in 70F (21C), it should be warm enough to dunk your plant. I have lost some of my tilly's before and I surmised, it is my prevailing temps..wrong timing when I watered!
Interesting though, I have been observing my tilly's outdoors, they can take the cold as long as dry, they are sheltered in my growcamp which is unheated. Our cold temps here is at times at 35 to 40F overnight very mild, thankfully no low 20's and they get some nice filtered sun during the day, so it survives well. I guess it is able to grab needed moisture at night when it is cooler.
Oh good to to know the other one has no lid! Good luck on your tilly's!