Poor Little Warrior! by Brian W. Aldiss (F&SF, April 1958) sees a time-travelling Claude Ford hunting a brontosaurus in the past:
You crawled heedlessly through the mud among the willows, through the little primitive flowers with petals as green and brown as a football field, through the beauty-lotion mud. You peered out at the creature sprawling among the reeds, its body as graceful as a sock full of sand. There it lay, letting the gravity cuddle it nappy-damp to the marsh, running its big rabbit-hole nostrils a foot above the grass in a sweeping semicircle, in a snoring search for more sausagy reeds. It was beautiful: here horror had reached its limits, come full circle and finally disappeared up its own sphincter. Its eyes gleamed with the liveliness of a week-dead corpse’s big toe, and its compost breath and the fur in its crude aural cavities were particularly to be recommended to anyone who might otherwise have felt inclined to speak lovingly of the work of Mother Nature.
This intensely described and emotionally heightened narrative continues, with descriptions of the scene alternating with Claude’s inner thoughts, until (spoiler) he eventually shoots and kills the creature. Then, as he examines the dinosaur’s body up close, one of the beast’s parasites attacks and kills him.
This seems to be more of a dramatic prose poem than a story, but maybe that, and the ironic ending, will do it for some readers. It’s certainly got more depth and vibrancy than the other time travel pieces of the period.
** (Average). 2,400 words. Story link.