A catheter tip electrode has a tissue contacting surface which electricallyconducts RFenergy to the tissue and is more thermally conductive than adjacent non-electrically conductivecoating or cover which prevents RF conduction to the tissue contacting thatsurface. The tipelectrode has a shell with a nonablating hollow proximal neck portion and adistal ablating portiondefining a fluid chamber, and a plug-like support member which is configuredwith a fluid channelon its outer surface so a fluid passage is provided between the member and theneck portion forconvective or direct cooling of the nonablating neck portion and nonconductivetubing covering it.