You do not need to keep everything cool when you are rubbing fat into flour for shortcrust pastry, but even if your hands are not naturally cool (and few people's are) you can keep everything else cool, chill the mixing bowl for about 30 minutes beforehand and use iced water to make the dough. A marble slab is excellent for rolling out pastry as the surface remains cold.
You could also buy an inexpensive gadget called a pastry blender that rubs in the fat for you. Hold the handle and draw the rack of rounded metal blades across the flour and fat until the mixture resemble breadcrumbs. The water can then be added and mixed in with a round-bladed knife or fork. Grating the chilled butter into the flour also reduces the rubbing time and hence the heat generated.
Or try a quick-mix pastry where you do not have to use your fingers. Sift 250g (2 cups) plain flour into a bowl with a pinch of salt. Using a fork, cream 150g butter at room temperature with 1.5 tablespoons of water and half the flour until well mixed. It takes about 30 seconds. Stir in the remaining flour to form a firm dough, then knead it on a lightly floured work surface until smooth. Or use frozen pre-rolled pastry sheets.