We report the first results from a search for transiting warm Jupiter exoplanets-gas giant planets receiving stellar irradiation below about 10^8^ erg/s/cm^2^, equivalent to orbital periods beyond about 10 days around Sun-like stars. We have discovered two transiting warm Jupiter exoplanets initially identified as transiting candidates in K2 photometry. K2-114b has a mass of 1.85_-0.22_^+0.23^ M_J_, a radius of 0.942_-0.020_^+0.032^ R_J_, and an orbital period of 11.4 days. K2-115b has a mass of 0.84_-0.20_^+0.18^ M_J_, a radius of 1.115_-0.061_^+0.057^ R_J_, and an orbital period of 20.3 days. Both planets are among the longest-period transiting gas giant planets with a measured mass, and they are orbiting relatively old host stars. Both planets are not inflated, as their radii are consistent with theoretical expectations. Their position in the planet radius-stellar irradiation diagram is consistent with the scenario where the radius-irradiation correlation levels off below about 10^8^ erg/s/cm^2^, suggesting that for warm Jupiters stellar irradiation does not play a significant role in determining the planet radius. We also report our identification of another K2 transiting warm Jupiter candidate, EPIC 212504617, as a false positive.