Actually, you should not have any trouble measuring anywhere in a "room" from the outside of that room if you are using an AD594 which has sufficiently high impedance to negate IR losses in fairly long wire itself.
The best setup would be to use have a TC cable with a long enough pigtail to reach your 594 directly. You then take out the variable of in-between connections.
But if you need to extend an existing thermocouple, you must use the same kind of wire for each of the wires to be extended and use thermocouple connectors classified for the type of thermocouple you are trying to extend. Dissimilar materials in any connection, other than the junction itself, will introduce undesired juction voltages and large measurement errors. Manufacturers also make extension wire which is materially similar to the TC wire, adds small amounts of error (plus or minus a degree or so), but is cheaper than the TC wire if costs are an issue.
With regard to your second post, since you have a shield, connect to the board ground ONLY if your board ground is referenced to earth ground. But if you are powering with an isolated supply, there will be no place for the noise to go (e.g. stray RF) but back into the power supply. Otherwise connect the shield directly to known earth ground. Also unless you have twisted TC wire and extension wire be careful to stay away from electromagnetic interference sources (motors, other electronics, fluorescent light fixtures, etc.).