A couple of things -
Unless the fluid, pipe and surrounding air are all at the same temperature there will always be some kind of temperature gradient. If the fluid is hot, relative to surroundings the very center will likely be hottest, the fluid touching the pipe wall will be coolest, the outside of the pipe wall will be cooler than that - and so on. Where this might play out is if you suddenly turned on some hot water and it flowed thru cold pipes the water would be cooled and the pipe heated. If you were to look at a cross section you'd see the differences.
A reasonable question might be to ask where in this cross section is of greatest interest - the center, the outside, etc? Don't forget that the fluid might be cooling as it travels down the pipe, especially if the initial temp just went up and the pipe hasn't warmed all the way along it's length.
The whole point of this is to illustrate why measuring the pipe wall temp might be sufficient. Now and then very low thermal mass sensors are placed in fluid streams but it's more common to have a T fitting and a well - more or less a protrusion into the fluid stream with a hole in it where the sensor resides.
If your sensor is small enough you might fabricate your own well. Thin wall copper or brass tubing could be inserted thru the pipe wall and soldered in place. The sensor could be packed into it with some thermal grease. That might give you somewhat faster response but also the separation you desire from the fluid stream.
If the pipe has a rather thick wall (castings of some faucets do) you might fashion a well from threaded brass rod (small dia). You'd drill/tap the thick wall. You'd drill out a pocket in the brass rod for a sensor.
Hope this is of some help.