Later, way below from where I was sitting, Trabants and BMWs snaked along spruce, suburban streets. Swathes of melancholy pine forest stretched towards Russia under a clear blue August sky. The sun sparkled on the unruffled, grey waters of the Baltic as the temperature needle climbed to a stultifying 110 degrees. I had this take on reality by being in a sauna with a window on the world - on the 26th floor of the Hotell Olumpia, to be precise.
Mihkel, my companion in this northern tropical hideaway, poured more water on to the stove. The extra heat hit the wooden roof, swept down and thwacked my head. I wondered why the glass didn't steam up, but the red funnel on the ferry easing its way out of the harbour on its short voyage to Helsinki stood out as clearly as ever.
If God ever needed to relax after work, he'd come here. He'd get in free but at 95 kroons (pounds 4.75), it's within reach of most mortals. I plunged into the pool, it too having a panoramic view of the capital with its "onion" domes and majestic spires.
Back in the changing room Mikhel, a journalist with Eesti Ekspress, bemoaned Estonian political affairs. "Everything you read is about the economy overheating, and the banking sector is out of control," he said. Bearing in mind the country has experienced at least six collapses of government, the statistics make impressive reading: 4 per cent unemployment, 5 per cent annual growth, a drop in inflation from 1,000 per cent in 1992 to around 10 per cent today.
Everywhere cranes swung across the skyline while builders' hammers and pneumatic drills rattled the late summer air. The huge lake of Ulemiste hangs above Tallinn and legend has it that the dastardly Old Man who lives there is waiting for the day when the city is finished so that he can let loose its waters and flood it. But judging by the extent of the construction work going on, he'll have to wait a good while yet.
"The heart of the old city is Raekoja plats, which has the only surviving Gothic town hall in northern Europe," the guidebook said. I looked around at the paved courtyard and realised this was it: I had to adjust to Estonia's minimalism. Tallinn, one of the few medieval cities still wrapped in its defensive walls, is an easy place to like.
The town hall was a perfectly preserved medieval building with its finger- thin spire pencilling the sky. In an upstairs room, the guest book revealed the signatures of Gorbachev, Dan Quayle and the Dalai Lama. I don't know if it was summer when the Dalai Lama visited but if it was, his Buddhist renunciation techniques must have been put severely to the test. In the summer, the beautiful, fathom-thighed girls of Tallinn wear mini-skirts so short it makes their 1960s cousins look like buttoned-up matrons.
Later, Toomas, a lugubrious ice cream seller, told me apologetically: "You see we have to pack all our sensuality into three months. It's too cold the rest of the year." I asked him whether Estonians were as reserved as people say. "Yes," he answered, and left it at that. But as I walked away, I caught him smiling. "But we always say what we mean," he added.
Perhaps it's their love of nature (eco-tourism flourishes), the lonely rural life that goes back centuries, and that only Finns understand their tricky language that makes them reserved. "You always know where you are with an Estonian," said an American I met. He liked their quietness, and so did I.
Pikk street curves away, art nouveau guild houses on either side. The former KGB block faces up to the 16th-century Oleviste church, whose architect fell to his death from its tower. The sombre location on Pikk street is about the only thing the two buildings shared, except that now the fabric on both is crumbling.
At the end of Pikk, stands the Fat Margaret Bastion, a round squat tower, one of the gateways to the old town. Beyond it, towards the harbour, standing in a garden is a quiet, white cross, erected as a monument to the 900 people who lost their lives in the ferry disaster of 1994.
At St Hubertus restaurant I found what I wanted: unadulterated Estonian food, garnished with reticence. A moose head greeted me from above the fireplace. I had eel soup, roasted wild boar in soya and honey sauce, with wild mushrooms, redcurrants and prunes. For afters I went for Talututar (country girl's sweet), grated ryebread roasted with sugar and lashings of loganberries and cream. With two glasses of Saku beer and coffee, it cost pounds 12. "Thank you," I said to the waitress, "that was very good."
"I know," she said.
Outside scores of people were clutching bouquets of flowers, some speaking into mobile phones at the same time. It was 6pm and flower-power time, when Estonians go visiting and tradition demands they take a bunch of flowers as a gift. But was it the meal or the music that made me grin all the way through the violin and organ concert at the Puhavaimu church? I don't know, but I do know that the 15th-century clock, carved altarpiece and pulpit are worth dropping in to see.
Estonians love their music, and you hear it at every turn. Many say the Singing Revolution of 1988-1991, when thousand-strong choirs gathered to sing folk songs, was a decisive factor in the Soviet Union relaxing its grip. When I was there, the blue, white and black national flag fluttered everywhere to mark the day, six years ago, when the country declared independence.
For my day trip to Parnu, the country's chic resort, I took the local bus, which swept past unfenced meadows sprinkled with wild flowers and red and yellow farmhouses. This Baltic spa used to be a summer retreat for Communist Party apparatchiks who came for its sanatoriums - Tchaikovsky used to stay up the road too. Locals have had the last laugh though - they've turned the old party headquarters into an arts complex, which they've whimsically called the Charlie Chaplin. The sugary white beach went on for miles, though when I stepped one pace beyond a sign saying "Women's Beach" a raucous cry greeted me from the ranks of female sunbathers. I think she meant scarper because when I looked closer, I saw the women were all, well, naked.
Back in the town square that evening, I drank a last Saku before leaving for the airport. The limousine and the greasers had gone and so, for that matter, had nearly everyone else. Where were they all? Then I remembered: Michael Jackson would be just starting his set. These days nothing in Estonia stays still for long.
estonia fact file
Estonian Air (0171 333 0196) operates flights from London (Gatwick) six days a week, from pounds 250 return including tax. Reduced fares available when booked with hotels.
Robert Nurden travelled with Estonian Air and Regent Holidays, tel: 01179 211711, fax: 01179 254866. Twelve-day Historic Baltic Tour of Estonia, Latvia and Lithuania from pounds 995, plus tailor-made holidays for the independent traveller, prices on request. Martin Randall (tel: 0181 742 3355; fax: 0181 742 1066) offers 10-day tours of Baltic states from pounds 1,490. No visas required.
Where to stay
Hotell Park: pounds 60 for twin, pounds 50 for single.
Hotell Dzingel: pounds 34 for twin, pounds 25 for single.
Where to eat
Vanaema Juures, Rataskaevu 10/12, Thirties lunchroom.
St Hubertus, Dunkri 6, traditional fare.
Where to drink
Nimega Baar, Suur-Karja 13, packed every night.
Diesel Boots, Lai 25, for the American way of life.
`Lonely Planet guide to Estonia, Latvia and Lithuania', pounds 12.99.
`Bradt Guide to Estonia', pounds 10.95.Reuse content