If I am reading your post correctly, you want to put 2 electric
baseboards with their own T-stat in a 10' by 10" room. Why not just put
a single 6 foot or 8 foot baseboard with one T-stat? If you go this
route, then you will probably need 220V. There is no relay needed since
the T-stats you will be using are line voltage types. But you
definately have to run a new circuit to the breaker panel for the
electric heat.