ASTM Standards: Steel Rod and Wire. Standard Specification for Steel Wire, Cold-Drawn for Mechanical Springs. Standard Specification for Steel Wire, Oil-Tempered Carbon Valve Spring Quality.
There are a handful of mills capable of producing hot rolled steel rounds & wire coils, and Jade-Sterling Steel has long standing relationships with most of them.
If you want to beat long mill delivery times, Taubensee Steel & Wire Company supplies hot rolled rod coils in various forms and conditions. That's the Taubensee.