1. В то лето = That summer, i.e. summer of a particular year (BC, AD, doesnt matter, a particular year will be meant)
Летом = in the summer, summertime - Year is not important, season is specified.

2. в том лете - grammatically incorrect. The rule of declension and preposition use dictate в то лето. A simpler form is Тем летом (=That summer), which is very often used.