As Temperature rises, so would the pressure, this would work immediately, as heat from the sun reaches Titan's surface.
The atmospheric escape (and thus, pressure loss, as you describe it) would work on a much longer timescale.
We can make a few estimates to determine this timescale: On the most simplified level, the composition if Titan's atmosphere is that of Earth's - it's mostly molecular Nitrogen.
So the mean molecular weight $\mu$ would be the same. The temperature would be similar compared to Earth by assumption of your experiment, then the only important difference is the mass and radius of the two bodies, reducing the escape speed by a factor of ~10.
Titan has 2% of the mass of Earth, so the ratio of escape speed to thermal molecular speed at the exobase, from where molecules are lost, would approximately scale like $\sim 1/\sqrt{10}\approx 3.1$
To determine escape rates, those go roughly like $\sim \exp(v_{th}/v_{esc})$ and would thus increase by $\sim \exp(3.1)\approx 22 $, compared to today's level.
I don't know present estimates for the lifetime of Titan's atmosphere, but this factor would e.e. bring it down from 5 billion years to only 250 million years. That's really short, geologically speaking!
But of course it's not enough to affect you in your pressure suit on the surface. You'd rather be concerned about an overpressure than underpressure.