Would it not be more appropriate to consider the variation of density in this? At the stagnation point the pressure increase, for a given velocity, will be higher than that calculated by the Bernoulli (incompressible) equation. A more suitable solution to Euler's equation removing the restriction on variation in density along a streamline and instead allowing the density to vary with pressure (using the isentropic relations) gives us this solution, sometimes called the compressible Bernoulli equation (NACA), or the Saint-Venant equation (N. X. Vinh),
Subscripts 0 and 1 describe the total (or stagnation) and local (freestream) states respectively. Dimensionless gamma (ratio of specific heats) can be assigned the standard calorically perfect value of 1.4. M is Mach number; u is the velocity of the rigid body relative to the fluid.
I've included the solution with M^2 as the subject to illustrate that for a P0/P1 value of 2 the condition you seek (i.e. total pressure is twice that of static pressure) is temperature-independent (within the restrictions of a calorically perfect gas). At Mach 1, P0/P1 = 1.8929, and I should stress that the above equations are not strictly valid beyond Mach 1. They are however in very good agreement with the supersonic solution (Rayleigh supersonic pitot equation) up to about Mach 1.2.
Strictly for P0/P1 = 2, the first equation can be reduced to:
u^2 = 440.052 T
T is temperature in Kelvin.
At ISA MSL the condition P0/P1 = 2 is satisfied, according to the above, when u = 356 m/s, or 692 kt.