What if you freeze soda bottles filled with water? Will take a while for them to warm up, you can wrap one in a towel and lay it in his bed, cheap cooling system, it may work, if he is hot he may choose to lay against it and if it is too cold for him he will stay away. I know it works with heat, if we put hot water bottles wrapped during winter they lay against it when they are cold, just like heating pads ... it may work other way around too... you could try and let us know
, I would wrap in a towel to be safe and avoid cold burns.
XOXO