Are there hot springs near Chiang Rai, Chiang Mai or Pai that are accessible by public transport so one can go by himself, not using tourist agency, still having no personal car?

There's hot springs right through the area you mention.

There's hot springs right through the area you mention.

googled and found some Sankamphaeng Hot Spring is 25 kilometers from Sankamphaeng district and 40 km CM and also ROONG AROON HOT SPRINGS. Some 3 in CR.

I do not know if you know that there are Hot springs in Rannong. And there are facility's for people to bathe in them for free, also there are special areas that you can lay down on them to absorb the heat , A lot of old Thai people go there to relieve pain caused by old age and accidents , You can goggle them to look at them, (Rannong Hot Springs). There is a hotel 10 minutes walk from them . Called Suksan House. 0 7783 2585-- 089-873-5123, about 600baht a night , all the rooms are Immaculately clean , You can get a VIP bus over night, the hotel is about 4oomt from the bus station , and the springs are across the road from the Hotel

These are about 30kms out of Chiang Rai past Doi Hang on the Mae Kok. I don't know what you'd do about transport, you'd have to talk to the sorng taew drivers at the old bus station and try to do a deal for the day maybe.

The drive out there is great, and a real "Unseen Thailand" delight.