http://focus.ti.com/lit/ds/symlink/sn7408.pdf The 7408 can sink 16ma maybe enough for a small relay. The http://focus.ti.com/lit/ds/symlink/sn74hct08.pdf 3ma not enough. The 7408 is obsolete http://search.digikey.com/scripts/D...DM7408N-ND. But that is not the point.
You fixed points in the design base on incorrect assumptions about what the micro can do.

I where to look for a board for you what would I look for. One with 5 volt relays? Rated at 1 amp or 20? You still have not said what temperature sensors you are using, even the range -20 to 100F or 0 to 1000. For Air or water or gasoline? how fast you you need to read the temperature? to what resolution.
Other may have lost patience (Sorry but MTBF) but you are asking for others to give you something. But you are keeping secrets. Stefan Kanev gave you a schematic, but you did not comment on it.

Before I personal would take on an free internet project for a stranger, I would have to think it was very cool. My take is you though up a great idea for a product but do not know how to make it.

If you want help pick and issue like temperature and solve it. remember you may not get a consensus here. you will get different options and have to pick one.

I would like to help but am not sure how. And have invest way to much time in this thread.

I might recommend "Nuts and Volts" Magazine. Threr are lots of beginner programming articles.