The 21-year-old Rugby man who was arrested on suspicion of committing arson with intent to endanger life has been bailed until December while enquiries continue.
Emergency services were called to the blaze in Wentworth Road in the early hours of Thursday (November 15).
A woman and three children remain in hospital following the fire.
One of the children, a five-year-old boy, remains in a critical but stable condition.
Det Insp Paul Thompson of Warwickshire Police's major investigation unit said: "We're continuing to work with colleagues at Warwickshire Fire and Rescue to establish the cause of the fire, which we are treating as suspicious at this time.
"One man has been arrested and is currently helping us with our enquiries.
"We're continuing to appeal for anyone who has any information that could help us with our enquiries to get in touch. We'd especially like to hear from anyone who any CCTV, dash cam footage or mobile phone footage of the incident.
"I'd like to thank the local community for the assistance they gave to the injured women and children while emergency services were on route and for the support they have shown to investigators throughout the day.
"This incident has shocked the community; I would like to reassure them that we will continue to have a police presence in the area over the next few days as try to establish how the fire started and to provide reassurance to local people."
Anyone with information can call 101 quoting incident 29 of 15 November 2018.
Alternatively, information can be provided anonymously to the independent charity Crimestoppers on 0800 555 111.