Summer can be hot and sticky in Indianapolis—not intolerable, but not the best season, either. It can get up into the 90s F/30s C with humidity in the 55%-80% range, but the average summer temperatures run 60-85 F/15-29 C.
The best times to visit are May-June and September-October, when the climate is at its mildest. Although the weather can be unpredictable, late April is beautiful with daffodils, tulips and flowering trees. Expect daytime highs of 73-83 F/22-28 C in spring and 66-77 F/18-25 C in the fall. A sweater or light jacket will protect against cool evenings—mid-40s to mid-50s F/7-12 C. There's no distinct rainy season, so there should be lots of sunshine mixed with rain.
There's some snow November-March, with yearly totals running from 6 in/15 cm to 44 in/112 cm. There is potential for fairly fast and heavy snowstorms, so you'll want to check the forecast. Winter temperatures can be quite cold (0 F/-17 C), but normally range 17-39 F/-4 to 3 C.