Say you had a large bomb - take the 50 megaton Tsar Bomba. You then proceed to place it in the center of a spherical tank containing liquid hydrogen, and then detonate it. Could you start a fusion reaction inside of that tank (and roughly how big would that tank need to be)?
The first ever thermonuclear device, Ivy Mike, contained a tank with liquid deuterium (heavier isotope of hydrogen, the main isotope, protium, has too small fusion cross-sections). The fusion reactions in this tank were ignited by a fission bomb.
Note, that the main problem for obtaining a significant yield from fusion reactions is to contain fusion fuel long enough for it to fuse, rather than being dispersed by the explosion prematurely (then this would be called a fizzle). So, while simply placing the bomb inside the tank with liquid deuterium will produce some fusion reactions, large yields require careful design such as Teller-Ulam configuration.
When the nuclear bomb is ignited, the liquid hydrogen in the tank would evaporate instantly. The evaporation heat of liquid hydrogen of a tank of any reasonable size is negligible compared to the energy released even by a small (Hiroshima) 15kT TNT fission bomb.
Note after comment by @rob: That there won't be any significant fusion of ordinary hydrogen with hydrogen has been answered here: Fusion: Why deuterium and tritium?