We present a study , based on archival XMM-Newton observations , of the extended X-ray emission associated with the inner disk of M33 . After the exclusion of point sources with L _ { X } > 2 \times 10 ^ { 35 } { ~ { } erg~ { } s ^ { -1 } } ( 0.3-6 keV ) , we investigate both the morphology and spectrum of the residual X-ray emission , comprising the integrated signal from unresolved discrete sources and diffuse components . This residual emission has a soft X-ray spectrum which can be fitted with a two-temperature thermal model , with kT \approx 0.2 keV and \approx 0.6 keV , the cooler component accounting for the bulk of the luminosity . There is evidence that the X-ray emitting plasma has a subsolar metal abundance . The soft X-ray surface brightness distribution shows a strong correlation with FUV emission and since the latter serves as a tracer of the inner spiral arms of M33 , this is indicative of a close connection between recent star-formation activity and the production of soft X-rays . Within 3.5 kpc of the nucleus of M33 , the soft X-ray and FUV surface brightness distributions exhibit similar radial profiles . The implication is that the ratio of the soft X-ray luminosity ( 0.3-2.0 keV ) per unit disk area to the star formation rate ( SFR ) per unit disk area remains fairly constant within this inner disk region . We derive a value for this ratio of 1 - 1.5 \times 10 ^ { 39 } { ~ { } erg~ { } s ^ { -1 } } ( \hbox { $ ~ { } M _ { \odot } $ } { yr } ^ { -1 } ) % ^ { -1 } , which is towards the top of the range of similar estimates for several other nearby face-on spiral galaxies ( e.g . M51 , M83 ) . In the same region , the ratio of soft X-ray luminosity to stellar mass ( the latter derived from K-band photometry ) is 4 \times 10 ^ { 28 } { ~ { } erg~ { } s ^ { -1 } } \hbox { $ ~ { } M _ { \odot } $ } ^ { -1 } , a factor of 5-10 higher than is typical of dwarf elliptical galaxies ( e.g . M32 , NGC3379 ) , suggesting that 10-20 % of the unresolved emission seen in M33 may originate in its old stellar population . The remainder of the soft X-ray emission is found to be equally split between two spatial components , one which closely traces the spiral arms of the galaxy and the other more smoothly distributed across the inner disk of M33 . The former must represent a highly clumped low-filling factor component linked to sites of recent or ongoing star formation , encompassing H II ~ { } regions , X-ray source complexes and X-ray superbubbles , whereas the distribution of the latter gives few clues as to its exact origin .