For an introductory book, tough to beat Schroeder's Introduction to Thermal Physics. Another book I thoroughly enjoyed reading back when I studied the stuff is Herbert Callen's "Thermodynamics and an Introduction to Thermostatics". Landau Lifshitz' Statistical Physics is a good read too, and goes in sufficient details while remaining accessible. There was a 4th book I studied too but I cannot remember the author's name (been many many years). I will edit this comment if/when it comes back to me.

I will personally recommend thermodynamics by Andrew steane. Great book and is written in a way so that it can be self studied.

If you liked Kleppner and Kolenkow, you might find Schroeder a bit too modern and Griffiths-y (sorry I'm not sure what the right adjective is here).

I think Kittel and Kroemer is a similar read, but it does require that you know the basics of quantum mechanics.

If you want a book on pure thermodynamics, somewhat ironically, Fermi's book might be your best bet. But it might be worth learning the standard physics sequence (mechanics to electromagnetism to quantum) to open up the possibilities.

With your math background you can jump straight into a rigorous thermo and thermal physics track using lecture notes plus one or two quirky classics, no PDEs required at the start.

If you liked Kleppner and Kolenkow because it feels clean and principled, the closest vibe in thermodynamics is the axiomatic style, start with Herbert Callen, Thermodynamics and an Introduction to Thermostatistics. It’s not trendy, it’s not cute, but it’s the book that makes the subject feel like a well built machine instead of a bag of tricks.

I’d lean hard on lecture notes from strong departments. The Oxford thermo notes are very approachable and keep the physics front and center.  É Brunet’s ENS notes are another great set, they’re the kind of notes that feel like someone actually tried to teach humans, not just impress the grader.  If you want something more physics grad flavored, Daniel Arovas has a big set of thermo and stat mech notes that are dense in a good way.

If you want a classic that’s short, sharp, and weirdly modern for its age, Enrico Fermi, Thermodynamics is a gem. It reads like a smart person explaining things on a chalkboard without trying to sell you a lifestyle brand.

If your brain likes building intuition first, then tightening the bolts, Blundell and Blundell, Concepts in Thermal Physics is a very solid bridge into the subject, lots of conceptual clarity without turning into hand waving.

What I’d do in practice, pick one notes set as your spine, Oxford or Brunet, and pair it with either Callen for the formal structure or Fermi for the clean narrative. Do problems aggressively, because thermo only becomes real when you start doing the differential gymnastics and Legendre transform moves on autopilot. You’ve already got the math to start, and you can learn the extra pieces as you go.

At my university we used the book “Fundamentals of Engineering Thermodynamics” by Moran, Shapiro, et. al. Not much math required though. It went over the basics & the first 2 laws of thermodynamics & then went into cycles & psychrometrics. If you are looking for harder material with more math involved you should probably dive into heat transfer then statistical mechanics.

I believe the gold standard for stat mech is Statistical Mechanics by Pathria & Beale but I haven’t read it yet.

Once you have a stronger math background, do yourself a favour and read Callen's book "Thermodynamics and an introduction to Thermostatistics". It's probably the best thermodynamics book ever written.