We conduct a multiwavelength continuum variability study of the Seyfert 1 galaxy NGC 5548 to investigate the temperature structure of its accretion disk. The 19 overlapping continuum light curves (1158 ˚A to 9157 ˚A) combine simultaneous HST , Swift , and ground-based observations over a 180 day period from 2014 January to July. Light-curve variability is interpreted as the reverberation response of the accretion disk to irradiation by a central time-varying point source. Our model yields the disk inclination i = 36◦ ± 10◦ , temperature T1 = (44 ± 6) × 103 K at 1 light day from the black hole, and a temperature-radius slope (T ∝ r −α) of α = 0.99±0.03. We also infer the driving light curve and find that it correlates poorly with both the hard and soft X-ray light curves, suggesting that the X-rays alone may not drive the ultraviolet and optical variability over the observing period. We also decompose the light curves into bright, faint, and mean accretion-disk spectra. These spectra lie below that expected for a standard blackbody accretion disk accreting at L/LEdd = 0.1. ; Support for HST program number GO-13330 was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. D.A.S. and K.D.H. acknowledge support from the UK Science and Technology Facilities Council through grant ST/K502339/1 and ST/J001651/1. M.M.F., G.D.R., B.M.P., C.J.G., and R.W.P. are grateful for the support of the National Science Foundation (NSF) through grant AST-1008882 to The Ohio State University. A.J.B. and L.P. have been supported by NSF grant AST-1412693. A.V.F. and W.Z. are grateful for financial assistance from NSF grant AST-1211916, the TABASGO Foundation, and the Christopher R. Redlich Fund. M.C. Bentz gratefully acknowledges support through NSF CAREER grant AST-1253702 to Georgia State University. M.C. Bottorff acknowledges HHMI for support through an undergraduate science education grant to Southwestern University. K.D.D. is supported by an NSF Fellowship awarded under grant AST-1302093. R.E. gratefully acknowledges support from NASA under awards NNX13AC26G, NNX13AC63G, and NNX13AE99G. J.M.G. gratefully acknowledges support from NASA under award NNX15AH49GHi Jonathan. P.B.H. is supported by NSERC. M.I. acknowledges support from the Creative Initiative program, No. 20080060544, of the National Research Foundation of Korea (NRFK) funded by the Korean government (MSIP). M.D.J. acknowledges NSF grant AST-0618209. SRON is financially supported by NWO, the Netherlands Organization for Scientific Research. B.C.K. is partially supported by the UC Center for Galaxy Evolution. C.S.K. acknowledges the support of NSF grant AST-1515876. D.C.L. acknowledges support from NSF grants AST-1009571 and AST-1210311. P.L. acknowledges support from Fondecyt grant 1120328. A.P. acknowledges support from an NSF graduate fellowship and a UCSB Deans Fellowship. J.S.S. acknowledges CNPq, National Council for Scientific and Technological Development (Brazil) for partial support and The Ohio State University for warm hospitality. T.T. has been supported by NSF grant AST-1412315. T.T. and B.C.K. acknowledge support from the Packard Foundation in the form of a Packard Research Fellowship to T.T.; also, T.T. thanks the American Academy in Rome and the Observatory of Monteporzio Catone for kind hospitality. The Dark Cosmology Centre is funded by the Danish National Research Foundation. M.V. gratefully acknowledges support from the Danish Council for Independent Research via grant no. DFF 4002-00275. J.-H.W. acknowledges support by the National Research Foundation of Korea (NRF) grant funded by the Korean government (No. 2010-0027910). This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with NASA ; Peer-reviewed ; Post-print