Cut each wine cork in half with a utility knife, making each half as even as possible to give the trivet an even surface.
Arrange the half corks in your pattern of choice by placing them next to each other with the circles face-up. For example, to form a small square trivet, make eight rows of eight wine corks.
Glue the corks together by running a hot glue gun along the side of each one and pressing the neighboring one into place. Repeat this until all of the corks in your pattern are connected.
Line the outside of the cork trivet with a ribbon. Fill the crevices between each cork with a line of hot glue and push the ribbon into place, making sure it fits around each cork. Let the glue dry overnight before using the trivet.
Cut a square or rectangle from plywood in the dimensions you desire for the trivet. Sand down any rough edges and fill in any indentations with wood putty.
Cut four sections from a piece of thin wood trim that are large enough to form a frame around the plywood. Place the wood trim around the plywood without attaching it and do a test layout of the cork pieces by arranging them horizontally within the frame. Make any adjustments to the frame location to accommodate the corks.
Place a line of wood glue onto each trim piece and press it into place on the plywood. Let it dry for at least six hours.
Paint or varnish the plywood and frame with a heat-resistant product and let it dry.
Fill in the space between the frame by gluing the corks horizontally in the same way as you test-fitted them in Step 2.