The black and white pet was discovered at the Stone Cross Shopping Centre on December 30 at 10.45am.
Now inspectors from the RSPCA have launched an appeal to try and find the culprits who dumped the kitten.
The nine-week-old kitten, now called Figaro, was rescued by a member of the public who took him home and alerted the charity.
Inspector Nichola Geraghty said: "He is recovering well and is in the care of a loving foster home but I would like to trace the person responsible for discarding him like a piece of rubbish down an alleyway in the cold - with no food or water.
"I am grateful to the man who found him and then kindly took him home to where he was kept safe and warm until we arrived."
Figaro is now in foster care arranged by the RSPCA's Coventry and District branch and comes amid an expected surge in pets being abandoned.
Dermot Murphy, head of the RSPCA’s animal rescue teams, said: “During the lockdown there have been reports of a rise in people buying or adopting new pets, often for the very first time.
"Whilst it’s great that so many people have become pet owners and have found their pet to be a real source of comfort during these challenging times, we are concerned that some people may have bought a pet on impulse without considering how their lifestyle might change once the pandemic ends.
"On top of that, we are facing real economic uncertainties, and, as in previous recessions, people may simply find themselves unable to afford their pet.
"The last thing we want to see is animals dumped and left out in the cold so we’d urge anyone who is struggling to care for their pets to please reach out to friends, family and charities for support instead."