Forget all about uncertainties at 0,06 °C for a TC-08.
First of all, the internal CJC (Cold Junction Compesation) is made ekstremely primitive. It is just a single thermistor in air in the middle of the converter box, so only when the temperature around and indside the TC-08 is totally stable, the CJC will work correct.
The only correct way to place the CJC is by a direct thermal connection to the mini TC sockets where the TC plug ends and TC wires convert to copper wires.
Secondly, type K TC have typically spec. af 2 °C or 1% (whichever is greater).
Type T TC is homewhat better, but have limited range (typ. 300 - 400 °C).
So my advice is:
Buy the TC's. Dedicate a specific TC to only the same input channel and get the system calibrated as a complete unit. Calibrate the unit in 4-5 temperature points, depending on your working range.
During calibration, secure that the temperature around the TC-08 is as stable as possible.
This can be achieved by placing the TC-08 in at isolated cardboard box.
Then use the readings and applied values stated in your calibration certificate as 'raw' and 'scaled' in a table look-up for 'calculated parameters'.
You now have 2 sets of temperatures. One set of the direct measurements and one set of the 'scaled' measurements, and it is easy to compare the 2 sets for eventually errors in the scaling, and it is also relativly easy to recalibrate again, as you can always read the direct measured values.
With this 'set up', I have managed to reduce the expanded uncertianity (95% K=2) to 0,3 - 0,4 °C with class 1 type T thermocouples in the range -100 to +300 °C.
As a professional within accredited calibration, I se no possibility get lower uncertainty with a Pico TC-08USB datalogger, unless you have a lot of historical data that confirms that your set is much more stable over time than e.g. 0,4 °C.
If your goal still is 0,1 °C or better, the only way with a Pico logger is a PT-104 and high quality RTD's (Pt100). I have with PT-104 and RTD's obtained an expanded uncertainty of 0,08 °C with the above mentioned method modified from table look-up to equation via a 3.rd degree polynomia and some clever Excel regression.
Excuse my bad English and the long answer, but talking of 0,06 °C/ 0,1% for a cheap thermocouple system, turned me somewhat on...