Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Indiana to Tegucigalpa as you normally would.
Due to multiple factors, expect to potentially pay more when booking in January. For low rates, July can be a great choice for travel to Tegucigalpa. Flights to Tegucigalpa from Indiana in July are about $778 on average during July, but can be found for as low as $288.