The server hosting my website doesn\'t have ffmpeg and I am not allowed to install any additional extensions. Is there any other way I can make video thumbnails dynamically?
Using external service won't be feasible, since even if you find one, you'll have to PUSH whole video to it and get the thumbnail results back.
I recommend you that you host your videos somewhere where you can install ffmpeg or some other utility that will produce your thumbnails, then access (reference) whole deal from your original server location.
EDIT:
Yet another alternative is to create thumbnails on the client. Can you describe what is the way of creating and uploading videos?
Sothink's Video Encoder Engine may do what you expect. It said on the product page that can auto create meaningful thumbnail image and Add PNG watermark image as logo. Hope it helps.
Try this: php video toolkit
See here:
http://www.facelooktube.info/wb/?category_name=svtm1
This software is created for creating thumbnails from video files. It can be used for video portals on low-cost servers without ffmpeg or you can use it if you need to replace auto created thumbnail of uploaded video.
Do it in the browser with HTML5's video tag and canvas: https://gist.github.com/adamjimenez/5917897