The T 2 was a Prussian standard design for a two-axle shunting tank locomotive. It was heavier than the T 1 and intended for service in medium and large stations. Henschel built a total of 67 directly for the Prussian State Railways between 1884 and 1889. None of these was taken over by the Reichsbahn in the 1920s. The LBE took delivery of four virtually identical locomotives between 1888 and 1892. Two came to the Reichsbahn as 88 7001 and 7002 and were retired in 1957. Another one delivered to the Bremen port railway in 1890 was later taken over by the Reichsbahn as 88 7601. One more was delivered to the Bredenbeck lime works, also in 1890.

The Oldenburg State Railway ordered a modified variant for use on branch lines. This had an increased top speed of 50 instead of 40 km/h and no steam dome, while the regulator had been moved into the smokebox. 38 were built by Hanomag between 1896 and 1913, 13 of which also had a continuous air brake. All but one were taken over by the Reichsbahn and became 98 101 to 98 137. All had been taken out of regular service by 1931, but a few worked on as works locomotives until 1953.