I've got type 2 diabetes and poor circulation

The link you provided is a company who sell hot water bottles! If I were you I’d look for some unbiased research.

A hot water bottle against cold skin can cause chilblains.
You'd be better off taking fairly warm showers and massaging arms and legs to get the blood flowing - after taking the Astra Zeneca covid jab my lower legs and feet were extremely swollen and a dreadful colour, but persisting with massage made a difference and I survived with all my toes which was actually quite a surprise. It does help to have a knowledge of anatomy, I think - encouraging blood up the veins and then down the arteries alternately and seeing feet deflating and toes changing from purple and white to something much more normal is very reassuring.
Recently, not having the winter fuel allowance we have had to reduce the heating, but have put an extra, lightweight duvet on the bed and bought a mattress topper and I have noticed how much warmer my feet have been. There must be more blood getting to them as my toenails have needed trimming more frequently - always a good sign.