The transmission puts out some heat, but you're more likely really feeling the heat from the catalytic converter which is next to the transmission. My suggestion is to just put the carpeting back in which is what I have done each time I was thinking I'll just live with the heat each time I tried pulling it out. I gave up on trying to run without the carpeting. Or glue some foil-backed insulation you can find in the roofing department of Home Depot, Lowes, etc. between the flooring & catalytic converter, engine, & transmission.