Hi Aamcle,
It's helpful to dintinguish precision (repeatability, or the smallest meaningful increment possible from a sensor) and accuracy (proximity of mean sensor output to the true value).
Thermocouples can in practice be extremely precise and accurate; as precise as PRTDs, in fact, if not more so. Their main limitation is that they measure temp at the measuring junction by reference to temp at a reference junction. ( A thermocouple is really a circuit with two wires, each of a different metal; if the 2 junctions of these diff metals are at diff temps, a voltage will be generated. In reality t/c circuits get far more complex but this is the principle.) So, your precision and accuracy are ultimately limited by whatever device (usually a cheap thermistor) is measuring temp at the reference jctn, and by the precision of whatever voltmeter is measuring the t/c voltage.
Any temp sensor can be calibrated to damn good accuracy by immersion in freezing or boiling water, which have known temps (accounting for altitude), and noting the offset; in general you'll find that both t/cs and PRTDs only drift noticeably in the zero, not the span. In other words, if your t/c reads 1.5 deg C in pure ice water at sea level, then you're pretty safe just subtracting 1.5 from the reading to get true temp. To do even better you can compare readings in ice water and boiling and get both a scale and offset correction. Even betterer, make measurements across a range of temps using a thermometer you know is accurate, fit a polynomial to the data and off you go.
In my field we use thermocouples to measure temp diffs on the order of 0.001-0.002 deg C. The limiting factor is your reference junction temp, not the thermocouple. If you want both accuracy and precision, then, your best bet is to make a simple t/c circuit with the PRTD (which is usually quite accurate) at the ref junction, and convert the t/c voltage to temp using the appropriate polynomial (easy to find with Google). For 0.1 deg C precision this would require around 0.005 mV precision in your voltmeter.
Is your thermocouple plugged into a standard multimeter, or something more advanced like a datalogger of some sort?