I found that I needed to have a heater on for my little feller at night when 10-15 degrees, as he was very cold most of the time. Not meaning to criticise or say anything bad, you did a wonderful thing, I was in the same boat with my little friend passing a few days after yours. I didn't realise myself for a while how much warmth these birds need, I spent hours taking to the animal hospital and he got so cold in a cat box with towels.. it was around 15-20 degrees celcius and he was so cold by the time I got back from the animal hospital. After that, I found that unless I left the heater on he would get cold and be cold to the touch.
It was very sad for me in my friends last days, the new apartment I moved into has free heating, but it is very unreliable and stopped working. I had thought it was on, but after a day noticed it wasn't, so he was very cold all this time, then another night he was cold before I realised to get the heater. This was not what caused him to pass at all, it was his injuries and the reason both you and I pick up these birds - because we are able to do it, they are usually very injured.
But I was glad that for the last day, I had noticed the broken heater and replaced with a small strip heater, so that he was at least warm for his final hours
I am still so devastated by the loss of my pigeon. I hope you are doing ok.
Many blessings upon you for your help and compassion and your time to share your story here.