Yes, that's the concern. A typical semi-precision fixed resistor will have a temperature coefficient of 50 or 100 parts-per-million-per-degC. Over the test temperature range of 40C then, it would change by either 0.2 or 0.4%. The Thermistor changes by 0.2% per degC (roughly), so this amount of variation in the "fixed" resistor would be too much. It's really not that much trouble to attach the wires.
Also, keep in mind that since I'm doing this measurement over a very wide temerature range and the resulting corrections are quite small (0.5C or less) that errors in my measurement of the freezer and room temperatures have to be very large to have a significant effect on the outcome. I already have an OS wireless sensor in the freezer and as long as it is within 2-3C I'm good to go.
Certainly you can use your ohm-meter with any thermistor. If you have an interchangeable unit with calibration table that's all you need. If you don't have the calibration table it would be very difficult to do it yourself (even with 2-3 good calibration points) because you don't even know what the actual curve looks like.
If you plot the logarithm of thermistor resistance against the inverse of absolute temperature (e.g. Kelvin or Rankine) you get something that's close to a straight line. The slope of that line (between 0C and 50C usually) is called beta-k. But if you want say 0.1C accuracy, then it is not really a straight line; a high-order polynomial can be fit to that with pretty good accuracy so you don't need the calibration table though. Anyway, without data from the mfr, or your own adjustable accurate temperature reference, just measuring 2 or 3 points on the curve is not good enough to nail down the whole curve.
The US Sensor thermistor in question changes resistance from 10,000.00 ohms to 10,021.95 ohms from 25.00C to 25.05C. If your DMM has a 1-ohm resolution and perhaps 2-5 ohms accuracy at 10,000 ohms (0.02% - 0.05%) it would not significantly degrade the accuracy of the thermistor. These resistances are high enough that you would not need to worry about a 4-wire ohms measurement.
Everything needs to be clean and free of dirt, oil and other residues. At 0C for example where the thermistor is at 32k-ohms, all it would take is spurious parallel resistance of 13 meg-ohms to create an additional 0.05C error. You need to keep that unwanted stuff larger than say 60meg-ohms at 0C to avoid additional errors. And it gets worse the colder you go.
You can learn more about thermistors at many places on the internet. I think US Sensor has some educational materials and so does Omega (
www.omega.com). Or just do an internet search...
Also on the subject of mesuring temperature to high levels of accuracy, measuring air temperature to an accuracy of say 0.1C is an interesting proposition. If you had a probe that could accurately and instantly measure the temperature at one small location like the head of a pin, you would get a surprise. The spot temperatures would fluctuate widely over time and position (at least several tenths C, perhaps more) in a normal room with quiet air. There are little pockets of warmer and cooler air just floating around all the time; I tried this with a thermistor and was surprised how noisy the measurements really are. I wound up adding a thermal mass (small piece of brass) to the thermistor just to filter out the short-term temperature fluctuations. I think this is partly why OS sensors have the thermistor inside a small plastic pocket with limited access to outside air -- that also acts like a low-pass filter to reduce the short-term fluctuations.
You may see a reference to a "well-stirred oil bath" on some of the thermistor and high-accuracy thermometer data sheets. They have found that if you place a thermistor in an oil bath with a known accuracy thermometer, the oil bath must be well-stirred to eliminate temperature differences between the two thermometers. Even in a liquid like oil, there can be significant temperature changes over short distances if the oil is not continuously stirred.