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You lucky people, how I envy you! I've not been to Alaska in June, but last year Spitzbergen (about the same latitude) was quite chilly, around freezing point or just below. With the added wind chill on the ship you'll need layers to keep warm, plus a water proof and wind proof top coat. I took boots for ashore as trainers are not very warm. You'll have a fantastic time, please write a review when you get back!
The max temp of 22 degress was in 1999 last year the average for the month of June was 16/20 degrees centigrade by day and around 8/10 degress at night. What it will be this June well likely in the range above from that you can judge what clothing to take.
The temp range for the Canadian Rockies could be similar to Alaska, but on one day last June, it was max 16 degrees centigrade and min was 0 degress so Mr Cooke's advice is very wise indeed but having said that June or July is probably the warmest time to visit these areas.
Toronto will be hot (same latitude as Spain), Vancouver will be warm and gets lots of rain, Rockies varies with altitude but is usually dry and sunny during day and cooling at night. Remember Banff is 4,000ft altitude and thats in the bottom of the valley. In early June some of the higher lakes may still be frozen over. Brian.
We did an identical trip to this in July 07. Toronto was very hot - zero rain. (Make sure you do a trip to Niagra - Niagra town is a bit like Blackpool but the falls make it worthwhile - a nicer place to stay is Niagra-on-the-lake.) I assume that you then fly to Calgary. Calgary was cooler than Toronto and I didn't think it was as nice. The Rockies tour is fantastic. In June Lake Louise and Lake Moraine may be iced over but still very impressive. We didn't have any rain during our tour. Wear layers as the temperature can fluctuate by the hour. The same applies to Alaska, when we went the weather was really good and we had very light rain on one occasion. Some days ashore were short sleeve weather, others we needed light jackets. If you do the whale watch you will need thick, warm clothes - hats gloves etc. You will have a wonderful time and see some marvellous scenery.