Is 10°C 10 times as hot as 1°C?

No.

Multiplying kelvin is fine because kelvin is an absolute scale.

For a given baseline, perhaps yes?. Kelvin has its baseline inherent, for C you can pick what you like if you're clear about it. Perhaps. (Edit: and using only positive or negative temps as pointed out above)

Parent's spaghetti examples weren't the most illustrative.

What I believe they're griping about is that "10°C does not have 10x as much heat as 1°C."

In actuality, "10°C has 10x the difference in heat that 1°C has relative to the freezing point of water."

So it's a comparison definition quirk, not a numerical one.

    c = k + 273
    x * c = x * k + x * 273

  1 Celsius = 274.15 Kelvin
  10 Celsius = 283.15 Kelvin

But that's not what's being said, per my lower comment -- it's 10x the difference relative to the freezing point of water, compared to 1°C.

The original upthread comments I were taking issue with were saying that multiplication has no meaning / is invalid in Celsius.

It does have a meaning, and it's mathematically consistent.

It may not mean what's being assumed, but nuance doesn't mandate "thou shalt never," IMHO.

The origin with celsius isn't at zero, so you're prevented from doing what you were pretending was multiplication (at least in the most natural way of doing it).

Obviously you can negate your offset, multiply and reapply your delta.

It's a bit damned awkward though.