Hi Rose! I seriously doubt they will grow in your sun room unless it receives a ton of light and is warm. Gaillardias grow in full sun and like it nice & warm so it's doubtful they will do well.
I am a strong believer in the simple fact is that what matters in this life is how we treat others. I think that's what living is all about. Not what I've done in my life but how I've treated others. ~~ Sharon Brown