Q:

How could I identify this thermistor

I've been scavenging for components on a deceased gadget and I've found a thermistor I'd like to use in the future. The problem is there's no serial code printed on it. Without knowing the manufacturer, finding the datasheet is going to be hard. I'm no EE, just a newbie. I'm assuming it is a thermistor because I've empirically verified that it resistance varies with temperature, and since it was inside  a cheap promotional gift I doubt they would have used a more expensive component. Here's a picture of it:

All I can tell for sure about it is that it is a negative temperature coefficient thermistor. I've taken a few measurements using my cheap multimeter and here are the values:

So my questions:

Have you ever seen one like this? Do you happen to know which brand (or possible brands) could it be?
Is there an online catalogue or DB so that I could identify the component just using the image and approximate resistance?
In case I failed at identifying it, could I infer the function given the plot? I mean, are these measurements consistent with the behaviour or a thermistor? (I was expecting a linear behaviour, but considering my results either one of the values is an outlier or the function is not linear)

NOTES:
First measurement was made with the resistor inside an ice cube (took several readings to be sure). I'm assuming the temperature here was close to 0ºC.
The last measurement was done with thermistor inside a glass of warm water. I measured the temperature using a digital clinical thermometer.
These two measurements are the most accurate readings I have been able to obtain with the available means at home. I'd have taken a few more readings using the clinical thermometer approach but it only shows me values in the range of 34-44 ºC, so they are too close to be useful. I was thinking about measuring again at boiling point (100ºC) but I've no means to measure the water temp at these levels. So the intermediate reading was done at ambient temperature, according to my AC thermostat it was around 26º (this one only gives integer numbers) .
My cheapo multimeter has an inherent resistance of measuring cables: 0.5 ohm and the precision is +-0.8%, but this is nothing compared to the errors in temperature reading so I doubt this info is meaningful.

A:

Looks like an 10kΩ NTC. Most NTC's aren't visibly branded, but the resistance at 25 degrees is the property that they are sold by.
Although chances are very slight that it is actually a Vishay part, this page lists a some datasheets for similar devices. Checking the datasheets for a similar part might give you a good feeling for how the device responds to temperature.

A:

Knowing that it is a 10k NTC is still a bit inexact. At least another important characteristic should be mentioned, the beta value. You can have two different 10k thermistors with different beta values, and they will give you different readings. So this is an important parameter to know, at least if you need accuracy and not just some ballpark temperature.
You have already determined that it is a 10k NTC by measuring it at 25 degrees (or close to it). To determine the beta, you need to make another measurement at another specific temperature, this is usually 85 degrees or 50 degrees (though there are others too, these are probably the most common). Then use the formula/calculator on this page to get the beta. The beta that you calculate this way won't be exact, but manufacturers only use specific betas, so take take a list of existing standard betas (for example look at the parametric search options at digikey), and the closest standard beta to your measurement will be yours. 
Some of the standard betas are so close to each other that you might only be able to narrow down your beta to 2 or 3 choices. Don't panic in this case, the reading difference between those is so small that your temperature error will be close to insignificant.

