The answer to both is yes.....
Do you mean a resistance thermometer? For example a platinum resistance thermometer? A PT100 thermometer has a known resistance at a set temperature e.g. a PT100 has a base resistance of 100 Ohms at 25 degrees Celsius or whatever - I can't remember exactly what it is - then there will be a coefficient of change in resistance with temperature. You would need to look these up. By passing a known current through the PT100 you can pick off a voltage, then use the voltage as an analogue input to Arduino. You could use a bit of Nichrome wire, but you would have to do the calibration.
There will be plenty of examples on how to do this.
Platinum resistance thermometry is the gold standard for industrial temperature measurements and I used them a lot, generally on a 4-20mA loop. The downside is that they are expensive. The output is generally linear. They come in 2-wire, 3-wire and 4-wire versions - the 3 and 4-wire versions allow you to compensate for lead resistance.
Thermocouples are also popular and come in many different types and temperature ranges. The biggest problem is that they have complex outputs that are not linear. Plus there are problems when you introduce new junctions i.e. Fe(iron) to copper. Again, widely used in industry, but generally with a thermocouple amplifier to do the hard work. They sometimes need a "cold junction"
If you want wide range accuracy, I would avoid thermocouples
There is a wide choice of alternative IC devices (analogue LM35, digital like Dallas DS18B20) all with pro's and con's. If you have to go down the resistance/thermocouple route then I would find some IC's to do the signal conditioning or you are going to end up with a lot of software maths