Mine is grumpy in the "morning" too, without fail. If it's the middle of the afternoon/early evening he is a little jumpy for a few minutes.

Also, I have a UTH under my rescue's tub, and I covered the adhesive side of it with aluminum foil and then duct taped it to the bottem. The middle of the UTH sags a little, but it still keeps my temps up and I haven't noticed the tape melting or losing adhesion so I'd say it's safe to tape it.