Seljavallalaug, which dates from 1923, is more basic. Set in a valley and backed by a cliff, with a snow-capped glacier beyond, it occupies one of the most stunning swimming pool positions on Earth. The water, at a family-friendly 36 degrees Celsius, is a deeper green than any I've been in before. We emerge two hours later with wrinkly fingers while a more recent arrival performs somersaults to assembled applause.

It is a regular feature of our trip that places which, on first sight, seem daunting become precious havens. En route to Heydalur, in Westfjords, a peninsula in the northwest that is geothermally rich but remote, we feel out of our depth. We are on a gravel track and have been driving for a long time. Crossing a mountain pass, we feel very vulnerable in our little hire car, with just a bag of snacks to sustain us.

Eventually the hotel Heydalur appears, a hillside of random outbuildings. Our family room is wall-to-wall single beds and mattresses, but over the next few days, thanks to its talking parrot and orphaned Arctic fox, warm welcome and fantastic home-cooked food, we come to really like the place. Fresh fruit and vegetables are still rare enough here that on the flight from London an Icelandic woman told me where I could buy them on our travels, but at Heydalur they are plentiful with our meals.

Heydalur has various hot pots and a swimming pool surrounded by cherry trees and roses, but at 6.30am I get out of bed for a more solitary experience. To reach a nearby hillside hot pot I have to cross a river before it becomes too high to navigate (more snowmelt comes downstream during the day, even with the midnight sun). It is a one-person pot surrounded by round stones and dripping moss and it is perfect: with the voo-voo-voo calls of unseen ground-nesting birds, snow-capped mountains on one side, a fjord on the other and bubbles of gas coming up through clear water.

Across Iceland, outdoor pools are often signposted - for swimming pools it's a man's head above three rippling lines; for hot pots a thermometer is added. Up here in Westfjords, many hot pots are more private, and the protocol is to ask at the neighbouring farm before you jump in. There are hose pipes pumping hot and cold water, allowing bathers to vary the temperature to their liking, and all come with some kind of shed (the wind can be bone-chilling).

We stop at fjord-side pots in Strandir, on rocky beaches strewn with giant pieces of driftwood from Siberian trees bleached by the elements. At Mjoifjordur the stripes of seaweed follow the contours of the shoreline in bright colours - lilac, red and gold. At Drangsnes the wind blows strong and wild.

Then we leave the peninsula and continue our journey through northern Iceland, back to civilisation, where there are houses actually next to each other and service stations serving hot dogs. We drive through horse country, passing wild ponies, and in shops, boxes of horse shoes are lined up at the cash till, next to the Durex and chewing gum.

Húsavik is a pretty clapboard port with humpback whales and dolphins out in the bay, and pizzas and cappuccinos in town. We spend an afternoon in a converted cheese tub on a cliff, surrounded by lupins, surveying the sea for whale tails.

At Hofsós, I swim just a few lengths in the geothermal infinity pool. (It's too hot for more: one of the surprises about swimming around Iceland is that it's often too hot for much actual swimming.)

At Mývatn, we have one last experience to tick off: to swim in a volcanic crater, where the water is an alluring turquoise. But swimming at this Viti crater (there are two, it transpires) is prohibited, and at the other one the temperature can often be too hot, so we go for the nearest volcanic swim we can find, Mývatn Nature Baths, north Iceland's equivalent to the famous Blue Lagoon near Reykjavik.

The smell is a bit eggy, but Iceland, I feel, has now been swum.

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