How to measure the temperature of a thin wire using a infrared (IR) thermometer?
Judging from the other post, you are designing an experiment, where you want to demonstrate the resistivity at different temperatures.  To do that, you need to know the temperature of the wire.  You don't necessarily need to self-heat the wire with electricity.

You've chosen a comfortable range of temperatures: between +10°C and +40°C.  You can touch this kind of temperature and it shouldn't hurt.  However, the room temperature is usually +18°C to +25°C, so you would need some method of chilling to get +10°C.

I would suspend the wire in a container filled with non-conductive liquid**.  The container can be large enough to measure with an IR thermometer.  You can also have a thermometer immersed in the liquid.  Have another container with warm liquid, and another one with chilled liquid.  You can move the wire from one container to another and measure the effect.  The temperature of the wire will equilibrate with the temperature of the liquid very quickly.

It could make sense to wind the wire on a plastic spool, being careful that the wire doesn't cross itself.  Perhaps, you could lay the wire into the thread of a large plastic screw.

** Silicone oil from the drug store, perhaps.  You could add some coloring to the liquid to make it look unusual.  Deionized water could work too, it has high resistivity.