I need a thermometer for a variety of different applications. As such, it has to be fairly precise (plus/minus 2 degrees) at different temperatures. Do I have to worry that, if I buy a thermometer which has a large range (0 to 300 C, for example), that it won't be sensitive to small changes in temperature near 40 C?
Thermometer Precision in Different Temperature Ranges
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With thin cuts of meat (like chicken breast or a steak), you want to make sure you put the thermometer in to the thin side of the meat so that the whole thermometer goes in to the meat, rather than putting it in through the "top" so that only a little of the thermometer is in the meat. If you're putting it in the top, you can get wildly inaccurate temperatures. Also make sure that the thermometer isn't touching a pan, exposed to air, or touching a bone. Any of those can have a negative effect.
Also, you only need to cook chicken to 74C / 165F. That may be part of the problem in your case.
You may also want to check that your thermometer is accurate. You can stick it in boiling water to check that it reads 100C / 212F (assuming of course it goes up that high).
I use the same hole if what I am checking is large, like a loaf of bread, and I don't want to poke it full of holes...although with my instant read thermometer, the hole is not particularly large.
If the hole is a large proportion to the item (big hole in the side of a cookie...I know, absurd, but you get the idea) where you think heat can run down that tunnel you've made, then be concerned, but I can't imagine any situations where it is likely that the thermometer hole is going to let enough heat in to alter the cooking.
I CAN imagine a situation where a thermometer in place could help transmit heat to the center and make it, potentially, cook quicker. We used to put a large nail in the center of a potato that we were baking in the coals of a fire so that the steel would help transmit heat to the center of the potato to make sure it got done evenly, but I don't know how much of a difference even THAT made.
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Best Answer
There are several type of thermometer. Since you didn't specify exactly what you will be using for the thermometer It's hard to tell which type you are getting. However the two most likely kind you will use are bulb thermometer and bimetal thermometer.
The way bulb thermometer works is there is a liquid inside of a thin tube. Heat expands the liquid so the higher the heat the more it expands. The liquid is calibrated to expand to the markings on the thermometer.
However, the sensitivity of a thermometer does not depend on it's range but rather on several different factors:
A bimetal thermometer operates on the principle that different metals contract and expand to different degrees when exposed to temperature changes. Two strips made of different metallic materials are fused together as a spiral or rod. The strip will wind, unwind or bend as the temperature changes because one of the two materials in the strip will contract or expand to a greater degree than the other will. The free end of the strip is attached to a pointer that will indicate the temperature.
Once again because the dial moves base on the expansion (this time metal) which will stay constant, the range of the thermometer will not be affected.
Please note that over time these metal might degrade and lower the sensitivity of the thermometer but that is an issue of the longevity of the equipment.
Also note that is it harder to read the smaller changes by the human eyes if the range is larger since is scale is smaller but that has nothing to do with it's sensitivity.
EDIT:
If by chance you are refering to the uncertainty of a thermometer or how "incorrect" a thermometer can be, as Rumtscho mentioned, the uncertainty is usually given in the specs of the thermometer and you will need to do some research to find the one that will fit your needs. Just for example Tel-Tru boast an uncertainty of just +/- 1/10th degree Fahrenheit for it's products. You can usually find this sort of information on the product's website.