Answer
No, the claim is false.
Work Step by Step
From table A-4 at $T=35^{\circ}C$
$P_{sat}=5.629kPa$
$P_{air}=\phi P_{sat}=0.7*5.629kPa=3.9403kPa$
Interpolating from table A-4 at $P=3.9403kPa$
$T_{sat}=28.67^{\circ}C$
The vapor in the air will condense at this temperature, since there's no condensation, the temperature is higher. So the claim that the temperature is $10^{\circ}C$ is false.
