What's you definition of "homemade PCB"?
If you don't mind soldering parts, you could use one of the various proto-shields (search for "proto" on shieldlist.org, there are dozens) along with a standard Arduino. You probably wouldn't want to use an Uno because of all the ADC (unless you multiplexed the thermometers), but a Mega has more than enough ADC cabable pins. You would need to wire up some circuitry (on the proto-board) to step-down the voltage on the six 10 VDC, but that's no problem using either transistors or voltage dividers (and you could use an opto-isolator on each if you wanted). For the seven 220 V/0.5 A outputs you don't even need relays. Since the current is only going to be about 0.5 A, a MOSFET rated for 250 V would suffice for each of those channels. You should be able to fit all the custom circuitry on either one Mega-sized proto-shield or two stacked standard proto-shields Top it off with an LCD, either on it's own shield or attached to the top of an enclosure, and you're good to go.