You should be and I would demand an RMA of that laptop. 105 is the max temp for that processor if it is near or over that temp you have a problem. I would demand to talk to a higher tier of help at HP if they are currently giving you the run around. You might talk to the retailer you bought from and see if they can do anything for you. Also sometimes if you paid with certain credit cards they have buyer protections built in.
Keep pursuing this with HP if it is under warranty and if they give you more run around, file a better business bureau report in Silicon Valley, CA.
Not blaming you by any means but this is why with Laptops I buy them at my local Micro Center and just buy the 3 year in store warranty. If I have an issue they credit you what you paid and you just go get another one. Dealing with these manufacturers these days is just brutal. They hope you just go away in frustration.
Good Luck!