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I ran the thermal calculations on equivalent stainless-clad, tin-coated, and uncoated copper cookware.

My Mauviel/Falk/Bougeat clad material measures 2.4mm copper, 0.1mm stainless steel. I assumed the same dimensions for the tin, but the math shows that even a difference of plus or minus 100% in the plating thickness is inconsequential.

The tin-lined laminate is one half of 1% more conductive than the stainless-clad.

An unlined 2.4mm copper pan is 1.6% more conductive.

If you think you notice these differences, I don't want your pans, I want what you're smoking.

deleted because of overcomplicated math/

Here's how to do the math, if you really want to think about the thermal relevance of the lining material.

The thermal conductivity of each metal, in W/(mK) [Watts per meter x degree Kelvin]:

Stainless Steel 16
Tin 67
Copper 401

If we look at similarly constructed pans, with 2.4mm of copper and 0.1mm lining material, we get a total conductivity per pan of:

copper/tin: 0.9691 W/K
copper/ss: 0.964 W/K

unlined copper: 0.9624 W/K

Which is to say, the tin-lined pan will conduct heat 1/2 of 1% faster than the stainless lined pan.

A completely unlined 2.4mm copper pan  conducts 1.6% faster than a stainless lined one.

If you can notice that difference, then you need more mattresses  between yourself and the pea than this princesses does.

My vote is that you're imagining it.