Preface: I am a noob to making precise measurements at home. So everything I state here is probably obvious to everyone.
Oddly enough I am just running into temperature related issues trying to measure the cell voltage of a Muirhead cell I salvaged from a local scrapyard. It serves a mental exercise to see if I can deduce from measurements if the cell is "good" or "not good". (I don't really need a 1ppm voltage reference at home - but it is a nice exercise to see if I can measure something with a predictable outcome).
I was getting 3-4uV swings in reading (which - if true - meant the cell should be scrapped).
I was pretty careful to ensure clean copper connecting to the cell (knurled nut) - but I didn't want exposed banana plugs getting shorted by accident so I used a Hirschmann safety banana (nickel over brass). These are large and therefore have a thermal mass (way more than I had given them credit). I underestimated Seebeck effect....
So I plotted V over 30 minutes or so:
Clearly it took over 10 minutes for the thermal effects to stabilize, and even then it would swiftly swing at any breeze. Covering it with cloth helped, but I am certain that unless I can control that junction temp (or replace the conductors with copper) - I will not be able to measure this with sufficient precision to answer the postulated question.
So to answer the OP question, to me it seems temperature is important in order to compensate for temp effects. I use it in my calculations. But as it turns out - even more important is to maintain thermal equilibrium at all costs. Cover all exposed connections, use highest gauge wire, keep all connectors together and at the same temp, if possible in a draft free box.
Oh - and ditch large brass and nickel contacts: As it turns out the Nickel Plated brass banana plugs can cause a drift of over 10uV given a nice temperature change as evidenced by using a cooler spray or hair dryer on the exposed areas of the banana....
Or - another option is to ignore the uV digits (if possible).