I too can't see keeping them in the same room, and would not personally reccomend reptiles in the same room as chins.
My chin room sits at 65, and the room my bearded dragon is in sits at a base temp of 72, and he then has his heat lamps on--which raise the temp of the actual room itself.
If you wash your hands, you should be fine. I've had Lincoln several years and have not had a problem . Beardies make awesome pets. They are like no other lizard thus far--mine has a ton of personality.
The biggest thing is to not get from a petstore, get from a reputable breeder. The other thing as a first time owner, I would suggest a juvie or adult beardies. Babies need much higher temps (105ish), and eat a TON- they cost a lot of money. Where as the adults can get away with a lower temp, and do not eat as much as a growing beardie does.