The EMF generated at the junction will drive the reading off-scale in one direction on most ordinary ohmmeters or multi-meters. The EMF is proportional to the temperature with respect to absolute temperature, so whether the engine is stone cold in the arctic or just too hot to touch in the desert, the variation of 230°K to 300°K doesn't make that much difference to the effect.
To get an accurate reading for thermocouples you need to use a bridge. The best results I've had were with a Wayne-Kerr capacitive bridge - which has a massive impedance. You balance the bridge for the dip position and note the first reading, then reverse the leads and repeat. The nominal value is then, just as you describe, the average of the two readings.