A synthetic population of single planet Hot Jupiter systems is generated by modeling tidal, thermal, and mass loss evolution with a random initial distribution of planet orbit, planet mass and stellar mass. Tides on stars act to move planets closer to their parent star, while tides on the planet are important in circularizing the planet and depositing energy inside the planet. The radius of the planet can temporarily be increased dramatically during the orbit's circularization. Mass loss through Roche Lobe overflow and evaporative, energy-limited mass loss are both modeled. The mass that is lost through the inner Lagrange point during Roche Lobe overflow creates an inner accretion disk around the parent star. Tides in this disk transport angular momentum to the planet, which can temporarily offset the effect of tides on the star. As there are strong selection effects that have gone into the distribution of observed transiting planets, an optimal match between the observed distribution and the synthetic population is not searched for. We do compare these populations to see if qualitative features in the observed distribution can be found in the synthetic population, specifically in the semi-major axis / planet mass plane and the planet mass / planet radius plane. The model predicts that although it is possible to achieve large radii, the fraction of planets that are expected to have such large radii is a small fraction of the total number of Hot Jupiters. These systems may require invoking perturbers that would continually drive the eccentricity and thus result in prolonged tidal heating inside the planet.