SR 362 then runs northerly along the western edge of Lake Loramie and Lake Loramie State Park before turning northwesterly then westerly and enters Minster and reaches its northern terminus at the intersection of South Main Street (SR 66) and First Street.

After passing the St. Michael's Catholic Church and several houses and business, the highway goes east out of town and enters farmland.

[3] In 1932, an unnumbered state highway following the general route of the modern-day SR 362 was established on the west side of Lake Loramie.

[9][10] This segment ran 1.5 miles (2.4 km) from Fort Loramie-Swanders Road north to the vicinity of Filburns Island.

Between 1955 and 1957, the discontinuous segment to Filburns Island was removed from the route and the southern terminus was moved to downtown Fort Loramie.