I recently ran into this problem when wanting to do temperature measurements with my HP 3456A.
After doing some research, the correct replacement is made by Measurement Specialties (acquired by TE Connectivity in 2014). The salient parameter is a beta value of 3976 for 25/85 or, as pointed out previously, a beta value of 3891 for 0/50.
From what I can tell, the direct replacement for the YSI 44007 is the TE Connectivity 44007RC, which is about $10 on Newark (70K8741) --cheapest I could find. It matches the 93.7 ohms at 150C given in the HP manual, the -80C resistance isn't shown in the R/T table unfortunately.
Using beta value 3976 and 5 kohm NTC as search parameters we find TE / Measurement Specialties "5K3A1 Series 1" for around $3 on Mouser (824-GA5K3A1A). It matches the 44007RC very well from 0C to 125C, but diverges slightly when going below 0C. And a similar 5K3A373I part on Newark (23M9110) for around the same price. Not a bad choice for low cost measurements above 0C, and moderately more accurate than using beta 3892 (0/50) parts. These parts essentially match the MAMAC Systems datasheet as uploaded earlier.
Digging through my parts bin turned up a NOS YSI 44034 thermistor, same as the 44007 with just slightly better accuracy. I had bought a lot of vintage gear from a cal lab that was closing shop a few years ago and nearly threw that thermistor away, lol. I'll still probably pick up a few 5k3A1 to have on hand and compare against the 44034.