Engine operates near 85°C (185°F) versus your 25°C (77°F). Lot of difference. Plus the 1-2 shift has to skip over the neutral detent on the shifter drum, where the other gears have no neutral detent between them. The oil is thicker at lower temp.
I traded my Z900RS for the XSR700 and one reason was the clunky gearchange (especially 6>5). To try and improve things I added Liquid Moly Motorbike Oil Additive
They specify 20ml per litre for wet clutches. It didn't help the clunk but it made the shift action much lighter. I should add that I always use synthetic oil.
My SV (now at 34k miles) has a fantastic gearbox and I have tried 3 different synthetic oils in the bike. Castrol Power 1 Racing, Smith and Allan Full Synthetic Motorcycle Oils | Smith And Allan and Motul synthetic (the dealer puts in at my request). The Motul makes the gearbox action even better, a fact I didn't think possible.
My XSR has done less than 2k miles but the shift action is very light and smooth hot or cold.