One of the cheap sticky strip thermometers for carboys would be fine. Stainless steel or any metal for that matter will conduct the inner temp through the metal very well. If you wanted to get fancy you could drill through the stainless and install a dial thermometer with o-rings.
I think I would put the sticky strip on the side and take a good quality lab thermometer and temporarily place it inside the fermenter to do a comparison. In general, glass does not conduct temperatures well at all and metals do so I would think the sticky strip would be good.
Congrats on the new hardware, That's what I want next.
''Once, I thought I was wrong, but I was mistaken'' (Read that somewhere, just loved it. Sorry if I stole it...consider it a compliment)
''I don't allow work during drinking hours''